Fuzzy Detour Convexity and Fuzzy Detour Covering in Fuzzy Graphs
Main Article Content
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.
Downloads
Metrics
Article Details
Licensing
TURCOMAT publishes articles under the Creative Commons Attribution 4.0 International License (CC BY 4.0). This licensing allows for any use of the work, provided the original author(s) and source are credited, thereby facilitating the free exchange and use of research for the advancement of knowledge.
Detailed Licensing Terms
Attribution (BY): Users must give appropriate credit, provide a link to the license, and indicate if changes were made. Users may do so in any reasonable manner, but not in any way that suggests the licensor endorses them or their use.
No Additional Restrictions: Users may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.