Application of Edge Detour Monophonic Number of a Fuzzy Graph
Keywords:
fuzzy graph, fuzzy strong chord, fuzzy monophonic path, fuzzy detour monophonic path, edge detour monophonic number.Abstract
In networks with uncertain or unreliable links, fuzzy graphs model link reliability. The edge detour monophonic number helps identify crucial nodes for secure detour routing when shortest paths are not viable. Let be a set of vertices in a connected non-trivial fuzzy graph . Then the edge detour monophonic closure of , denoted by , is the set of all edges lying on the fuzzy detour monophonic path between a pair of vertices of . A set M of vertices in a connected non-trivial fuzzy graph is defined to be an edge detour monophonic set of if , the edge set of . An edge detour monophonic set of minimum cardinality is called an edge detour monophonic basis of and the cardinality of an edge detour monophonic basis in is the edge detour monophonic number of , denoted by . The minimum number of vertices in a set such that every edge in the fuzzy graph lies in a monophonic detour path between two vertices in the set. In this study, the applications of edge detour monophonic number of fuzzy graph in the system of transporting goods are applied in order to optimize the number of commercial vehicle inspectors required to patrol and inspect the vehicle routes currently used in an urban road network.
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