Fuzzy Detour Convexity and Fuzzy Detour Covering in Fuzzy Graphs

A path P connecting a pair of vertices in a connected fuzzy graph is called a fuzzy detour, if its μ - length is maximum among all the feasible paths between them. In this paper we establish the notion of fuzzy detour convex sets, fuzzy detour covering, fuzzy detour basis, fuzzy detour number, fuzzy...

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Bibliographic Details
Published in:Turkish journal of computer and mathematics education 2021-04, Vol.12 (2), p.2170-2175
Main Authors: Rajeshkumar, R, Anto, A M
Format: Article
Language:English
Subjects:
Apexes
Convexity
Fuzzy sets
Graph theory
Set theory
Online Access:Get full text
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Summary:A path P connecting a pair of vertices in a connected fuzzy graph is called a fuzzy detour, if its μ - length is maximum among all the feasible paths between them. In this paper we establish the notion of fuzzy detour convex sets, fuzzy detour covering, fuzzy detour basis, fuzzy detour number, fuzzy detour blocks and investigate some of their properties. It has been proved that, for a complete fuzzy graph G, the set of any pair of vertices in G is a fuzzy detour covering. A necessary and sufficient condition for a complete fuzzy graph to become a fuzzy detour block is also established. It has been proved that for a fuzzy tree there exists a nested chain of sets, where each set is a fuzzy detour convex. Application of fuzzy detour covering and fuzzy detour basis is also presented.  
ISSN:1309-4653
1309-4653
DOI:10.17762/turcomat.v12i2.1898