Turkish Journal of Computer and Mathematics Education
Journal license

Journal

Turkish Journal of Computer and Mathematics Education


Volume
& Issue

Volume 12, Issue 2


Published
on

April 5, 2021


Pages

2170-2175


DOI

Article

Fuzzy Detour Convexity and Fuzzy Detour Covering in Fuzzy Graphs


Authors

R. Rajeshkumara Affiliation:
Research Scholar, Malankara Catholic College, Affiliated to Manonmaniam Sundaranar University, Tamil Nadu, India
and A.m. Anto Affiliation:
Assistant Professor, Department of Mathematics, Malankara Catholic College, Mariagiri, Tamil Nadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli – 627012, Tamilnadu, India.


Abstract

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.


Keywords

fuzzy detour, detour convex, detour covering, detour basis, detour number, fuzzy detour blocks


Citation

Rajeshkumara, R. & Anto, A. (2021). Fuzzy detour convexity and fuzzy detour covering in fuzzy graphs. Turkish Journal of Computer and Mathematics Education, 12(2), 2170–2175.

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