{"id":41260,"date":"2024-09-27T12:52:05","date_gmt":"2024-09-27T12:52:05","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%a7%d8%a8%d8%b9%d8%a7%d8%af-%d9%85%d8%aa%d8%b1%db%8c%da%a9-%d9%85%d8%aa%d8%ad%d9%85%d9%84-%d8%ae%d8%b7\/"},"modified":"2024-09-27T12:52:42","modified_gmt":"2024-09-27T12:52:42","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%a7%d8%a8%d8%b9%d8%a7%d8%af-%d9%85%d8%aa%d8%b1%db%8c%da%a9-%d9%85%d8%aa%d8%ad%d9%85%d9%84-%d8%ae%d8%b7","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%a7%d8%a8%d8%b9%d8%a7%d8%af-%d9%85%d8%aa%d8%b1%db%8c%da%a9-%d9%85%d8%aa%d8%ad%d9%85%d9%84-%d8%ae%d8%b7\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0628\u0639\u0627\u062f \u0645\u062a\u0631\u06cc\u06a9 \u0645\u062a\u062d\u0645\u0644 \u062e\u0637\u0627 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u06a9\u0627\u06a9\u062a\u0648\u0633 \u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0628\u0631\u06af \u0628\u0627 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0631 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0632\u0646\u062c\u06cc\u0631\u0647 \u062a\u0627\u0645\u06cc\u0646"},"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>\nFault Tolerant Metric Dimensions of Leafless Cacti Graphs with Application in Supply Chain Management<\/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 \u0627\u0628\u0639\u0627\u062f \u0645\u062a\u0631\u06cc\u06a9 \u0645\u062a\u062d\u0645\u0644 \u062e\u0637\u0627 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u06a9\u0627\u06a9\u062a\u0648\u0633 \u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0628\u0631\u06af \u0628\u0627 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0631 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0632\u0646\u062c\u06cc\u0631\u0647 \u062a\u0627\u0645\u06cc\u0646<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nTauseef Asif, Ghulam Haidar, Faisal Yousafzai, Murad Ul Islam Khan, Qaisar Khan, Rakea Fatima<\/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
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\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n20<\/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>\nDiscrete Mathematics,Combinatorics,\u0631\u06cc\u0627\u0636\u06cc\u0627\u062a \u06af\u0633\u0633\u062a\u0647 , \u062a\u0631\u06a9\u06cc\u0628\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 9 September, 2024; originally announced September 2024. , MSC Class: 05C12; 05C90<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 9 \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 \u06a9\u0644\u0627\u0633 MSC: 05C12 \u061b05C90<\/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
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\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

A resolving set for a simple graph $G$ is a subset of vertex set of $G$ such that it distinguishes all vertices of $G$ using the shortest distance from this subset. This subset is a metric basis if it is the smallest set with this property. A resolving set is a fault tolerant resolving set if the removal of any vertex from the subset still leaves it a resolving set. The smallest set satisfying this property is the fault tolerant metric basis, and the cardinality of this set is termed as fault tolerant metric dimension of $G$, denoted by $\u03b2'(G)$. In this article, we determine the fault tolerant metric dimension of bicyclic graphs of type-I and II and show that it is always $4$ for both types of graphs. We then use these results to form our basis to consider leafless cacti graphs, and calculate their fault tolerant metric dimensions in terms of \\textit{inner cycles} and \\textit{outer cycles}. We then consider a detailed real world example of supply and distribution center management, and discuss the application of fault tolerant metric dimension in such a scenario. We also briefly discuss some other scenarios where leafless cacti graphs can be used to model real world problems.<\/p>\n

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\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u06a9\u0627\u06a9\u062a\u0631\u06cc \u0628\u062f\u0648\u0646 \u0628\u0631\u06af \u0628\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0628\u0631\u062f\u0627\u0631\u06cc \u0627\u0632 \u0645\u0634\u06a9\u0644\u0627\u062a \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/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
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\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":"

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