{"id":41225,"date":"2024-09-27T12:42:28","date_gmt":"2024-09-27T12:42:28","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/"},"modified":"2024-09-27T12:42:29","modified_gmt":"2024-09-27T12:42:29","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPolynomials Counting Group Colorings in Graphs<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nHoushan Fu<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n14<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nCombinatorics,\u062a\u0631\u06a9\u06cc\u0628\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 18 September, 2024; originally announced September 2024. , Comments: 14pages , MSC Class: 05C31; 05C15<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0627\u0626\u0647 \u0634\u062f\u0647 \u062f\u0631 18 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: 14 \u0635\u0641\u062d\u0647 \u060c \u06a9\u0644\u0627\u0633 MSC: 05C31 \u061b05C15<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

Jaeger et al. in 1992 introduced group coloring as the dual concept to group connectivity in graphs. Let $\u0393$ be an Abelian group, $ f: E(G)\\to\u0393$ and $D$ an orientation of a graph $G$. A vertex coloring $c:V(G)\\to\u0393$ is a $(\u0393, f)$-coloring if $c(v)-c(u)\\ne f(e)$ for each edge $e=uv$ and the corresponding arc $D(e)=(u,v)$ directed from $u$ to $v$. We introduce the concept of $\u03b1$-compatible graphs and define the cycle-assigning polynomial $P(G, \u03b1; k)$ at $k$ in terms of $\u03b1$-compatible spanning subgraphs, where $\u03b1$ is an assigning of $G$ from its cycles to $\\{0,1\\}$. We prove that the cycle-assigning polynomial $P(G,\u03b1;k)$ equals the number of $(\u0393,f)$-colorings for any Abelian group $\u0393$ of order $k$ and $f:E(G)\\to\u0393$ such that the assigning $\u03b1_{D,f}$ induced by $f$ equals $\u03b1$. In particular, $P(G,\u03b1;k)$ is the classical chromatic polynomial if $\u03b1(C)=0$ for any cycle $C$ of $G$. Furthermore, we introduce the concept of $\u03b1$-compatible broken cycles and interpret $P(G,\u03b1;k)$ in terms of $\u03b1$-compatible spanning subgraphs that do not contain $\u03b1$-compatible broken cycles. This implies that the absolute value of the coefficient of $k^{r(G)-i}$ in $P(G,\u03b1;k)$ equals the number of $\u03b1$-compatible spanning subgraphs that have $i$ edges and contain no $\u03b1$-compatible broken cycles, which generalizes the Whitney’s Broken Cycle Theorem. Based on the combinatorial explanation, we establish a unified order-preserving relation from assignings to cycle-assigning polynomials. Finally, we show that for any loopless graphs $G$, the coefficients of the cycle-assigning polynomial $P(G,\u03b1;k)$ are nonzero and alternate in sign, and further conjecture that the sequence of absolute values of its coefficients is unimodal and log-concave.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u062c\u0627\u06af\u0631 \u0648 \u0647\u0645\u06a9\u0627\u0631\u0627\u0646.\u062f\u0631 \u0633\u0627\u0644 1992 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u06af\u0631\u0648\u0647 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0641\u0647\u0648\u0645 \u062f\u0648\u06af\u0627\u0646\u0647 \u0628\u0647 \u0627\u062a\u0635\u0627\u0644 \u06af\u0631\u0648\u0647 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u0645\u0639\u0631\u0641\u06cc \u06a9\u0631\u062f.\u0628\u06af\u0630\u0627\u0631\u06cc\u062f $ \u03b3 $ \u06cc\u06a9 \u06af\u0631\u0648\u0647 Abelian \u0628\u0627\u0634\u062f \u060c $ f: e (g) \\ to\u03b3 $ \u0648 $ d $ \u062c\u0647\u062a \u06af\u06cc\u0631\u06cc \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 $ g $.\u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc vertex $ c: v (g) \\ to\u03b3 $ $ (\u03b3 \u060c f) $-\u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0627\u06af\u0631 $ c (v) -c (u) \\ ne f (e) $ \u0628\u0631\u0627\u06cc \u0647\u0631 \u0644\u0628\u0647 $ e = uv $ $\u0648 \u0642\u0648\u0633 \u0645\u0631\u0628\u0648\u0637\u0647 $ d (e) = (u \u060c v) $ \u0627\u0632 $ u $ \u0628\u0647 $ v $ \u0647\u062f\u0627\u06cc\u062a \u0645\u06cc \u0634\u0648\u062f.\u0645\u0627 \u0645\u0641\u0647\u0648\u0645 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0633\u0627\u0632\u06af\u0627\u0631 \u0628\u0627 $ \u03b1 $ \u0631\u0627 \u0645\u0639\u0631\u0641\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0627\u0632 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc $ p (g \u060c \u03b1 \u061b k) $ $ $ $ $ $ $ \u0631\u0627 \u0627\u0632 \u0646\u0638\u0631 \u0632\u06cc\u0631\u06af\u0631\u0627\u0641\u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 $ \u03b1 $ $ \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u03b1 \u03b1 $ \u0627\u062e\u062a\u0635\u0627\u0635 \u062f\u0647\u0646\u062f\u0647 \u0627\u0633\u062a.\u0627\u0632 $ g $ \u0627\u0632 \u0686\u0631\u062e\u0647 \u0647\u0627\u06cc \u062e\u0648\u062f \u0628\u0647 $ \\ {0\u060c1 \\} $.\u0645\u0627 \u062b\u0627\u0628\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc $ p (g \u060c \u03b1 \u061b k) $ \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u062a\u0639\u062f\u0627\u062f $ (\u03b3 \u060c f) $-\u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0628\u0631\u0627\u06cc \u0647\u0631 \u06af\u0631\u0648\u0647 abelian $ $ $ \u0633\u0641\u0627\u0631\u0634 $ k $ \u0648 $ f: e (g) \\ to\u03b3 $ \u0628\u0647 \u06af\u0648\u0646\u0647 \u0627\u06cc \u06a9\u0647 \u0627\u062e\u062a\u0635\u0627\u0635 $ \u03b1_ {d \u060c f} $ \u0646\u0627\u0634\u06cc \u0627\u0632 $ f \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627 $ \u03b1 $.\u0628\u0647 \u0637\u0648\u0631 \u062e\u0627\u0635 \u060c $ p (g \u060c \u03b1 \u061b k) $ \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u06a9\u0631\u0648\u0645\u0627\u062a\u06cc\u06a9 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u0627\u06af\u0631 $ \u03b1 (c) = 0 $ \u0628\u0631\u0627\u06cc \u0647\u0631 \u0686\u0631\u062e\u0647 $ c $ g $ $ \u0628\u0627\u0634\u062f.\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646 \u060c \u0645\u0627 \u0645\u0641\u0647\u0648\u0645 \u0686\u0631\u062e\u0647 \u0647\u0627\u06cc \u0634\u06a9\u0633\u062a\u0647 \u0633\u0627\u0632\u06af\u0627\u0631 \u0628\u0627 $ \u03b1 $ \u0631\u0627 \u0645\u0639\u0631\u0641\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 $ p (g \u060c \u03b1 \u061b k) $ \u0631\u0627 \u0627\u0632 \u0646\u0638\u0631 \u0632\u06cc\u0631\u06af\u0631\u0627\u0641\u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u03b1 \u03b1 $ \u06a9\u0647 \u062d\u0627\u0648\u06cc \u0686\u0631\u062e\u0647 \u0647\u0627\u06cc \u0634\u06a9\u0633\u062a\u0647 \u0633\u0627\u0632\u06af\u0627\u0631 \u0628\u0627 $ \u03b1 \u0646\u06cc\u0633\u062a\u0646\u062f \u060c \u062a\u0641\u0633\u06cc\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u0645\u0637\u0644\u0642 \u0636\u0631\u06cc\u0628 $ k^{r (g) -i} $ \u062f\u0631 $ p (g \u060c \u03b1 \u061b k) $ \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u0632\u06cc\u0631\u06af\u0631\u0627\u0641\u0647\u0627\u06cc \u0633\u0627\u0632\u06af\u0627\u0631 \u0628\u0627 $ \u03b1 $ \u0627\u0633\u062a \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u0644\u0628\u0647 \u0647\u0627\u06cc $ $ \u0647\u0633\u062a\u0645\u0648 \u0634\u0627\u0645\u0644 \u0647\u06cc\u0686 \u0686\u0631\u062e\u0647 \u0634\u06a9\u0633\u062a\u0647 \u0633\u0627\u0632\u06af\u0627\u0631 \u0628\u0627 $ \u03b1 $ \u060c \u06a9\u0647 \u0642\u0636\u06cc\u0647 \u0686\u0631\u062e\u0647 \u0634\u06a9\u0633\u062a\u0647 \u0648\u06cc\u062a\u0646\u06cc \u0631\u0627 \u062a\u0639\u0645\u06cc\u0645 \u0645\u06cc \u062f\u0647\u062f.\u0628\u0631 \u0627\u0633\u0627\u0633 \u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0631\u06a9\u06cc\u0628\u06cc \u060c \u0645\u0627 \u06cc\u06a9 \u0631\u0627\u0628\u0637\u0647 \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u0628\u0631\u0627\u06cc \u062d\u0641\u0638 \u0646\u0638\u0645 \u0631\u0627 \u0627\u0632 \u062a\u06a9\u0627\u0644\u06cc\u0641 \u0628\u0647 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0647\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u0646\u062f\u0647 \u0686\u0631\u062e\u0647 \u0628\u0631\u0642\u0631\u0627\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0633\u0631\u0627\u0646\u062c\u0627\u0645 \u060c \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u062f\u0648\u0646 \u062d\u0644\u0642\u0647 $ g $ \u060c \u0636\u0631\u0627\u06cc\u0628 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc $ p (g \u060c \u03b1 \u061b k) $ $ nonzero \u0648 \u0645\u062a\u0646\u0627\u0648\u0628 \u062f\u0631 \u0639\u0644\u0627\u0645\u062a \u0647\u0633\u062a\u0646\u062f \u0648 \u0628\u06cc\u0634\u062a\u0631 \u062d\u062f\u0633 \u0645\u06cc \u0632\u0646\u0646\u062f \u06a9\u0647 \u062a\u0648\u0627\u0644\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0637\u0644\u0642 \u0636\u0631\u0627\u06cc\u0628 \u0622\u0646Unimodal \u0648 Log-Concave \u0627\u0633\u062a.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Polynomials Counting Group Colorings in Graphs \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"open","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[21],"product_tag":[],"class_list":{"0":"post-41225","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-21","7":"pmpro-has-access","8":"desktop-align-left","9":"tablet-align-left","10":"mobile-align-left","12":"first","13":"instock","14":"downloadable","15":"shipping-taxable","16":"purchasable","17":"product-type-simple"},"yoast_head":"\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-\u0631\u0646\u06af-\u0622\u0645\u06cc\u0632\u06cc-\u0647\u0627\u06cc-\u06af\u0631\u0648\u0647\u06cc-\u0634\/\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"og:description\" content=\"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Polynomials Counting Group Colorings in Graphs \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-\u0631\u0646\u06af-\u0622\u0645\u06cc\u0632\u06cc-\u0647\u0627\u06cc-\u06af\u0631\u0648\u0647\u06cc-\u0634\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-27T12:42:29+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png\" \/>\n\t<meta property=\"og:image:width\" content=\"440\" \/>\n\t<meta property=\"og:image:height\" content=\"486\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/\",\"url\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/\",\"name\":\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"isPartOf\":{\"@id\":\"https:\/\/express24.ir\/d\/#website\"},\"datePublished\":\"2024-09-27T12:42:28+00:00\",\"dateModified\":\"2024-09-27T12:42:29+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/#breadcrumb\"},\"inLanguage\":\"fa-IR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u062e\u0627\u0646\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/express24.ir\/d\/#website\",\"url\":\"https:\/\/express24.ir\/d\/\",\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/express24.ir\/d\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fa-IR\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-\u0631\u0646\u06af-\u0622\u0645\u06cc\u0632\u06cc-\u0647\u0627\u06cc-\u06af\u0631\u0648\u0647\u06cc-\u0634\/","og_locale":"fa_IR","og_type":"article","og_title":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","og_description":"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Polynomials Counting Group Colorings in Graphs \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc […]","og_url":"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-\u0631\u0646\u06af-\u0622\u0645\u06cc\u0632\u06cc-\u0647\u0627\u06cc-\u06af\u0631\u0648\u0647\u06cc-\u0634\/","og_site_name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","article_modified_time":"2024-09-27T12:42:29+00:00","og_image":[{"width":440,"height":486,"url":"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png","type":"image\/png"}],"twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/","url":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/","name":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","isPartOf":{"@id":"https:\/\/express24.ir\/d\/#website"},"datePublished":"2024-09-27T12:42:28+00:00","dateModified":"2024-09-27T12:42:29+00:00","breadcrumb":{"@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/#breadcrumb"},"inLanguage":"fa-IR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%86%da%af-%d8%a2%d9%85%db%8c%d8%b2%db%8c-%d9%87%d8%a7%db%8c-%da%af%d8%b1%d9%88%d9%87%db%8c-%d8%b4\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u062e\u0627\u0646\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":2,"name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":3,"name":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0646\u06af \u0622\u0645\u06cc\u0632\u06cc \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0634\u0645\u0627\u0631\u0634 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0647\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627"}]},{"@type":"WebSite","@id":"https:\/\/express24.ir\/d\/#website","url":"https:\/\/express24.ir\/d\/","name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/express24.ir\/d\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"fa-IR"}]}},"_links":{"self":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product\/41225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/types\/product"}],"replies":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/comments?post=41225"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media\/27"}],"wp:attachment":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media?parent=41225"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_cat?post=41225"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_tag?post=41225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}