Fuzzy Detour Convexity and Fuzzy Detour Covering in Fuzzy Graphs
| Autor: | R. Rajeshkumar |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Basis (linear algebra) Mathematics::General Mathematics Computer science General Mathematics Regular polygon Block (permutation group theory) Hardware_PERFORMANCEANDRELIABILITY Computer Science::Social and Information Networks Fuzzy logic Tree (graph theory) Convexity Education Set (abstract data type) Computational Mathematics ComputingMethodologies_PATTERNRECOGNITION Computational Theory and Mathematics Path (graph theory) Hardware_INTEGRATEDCIRCUITS ComputingMethodologies_GENERAL MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | Turkish Journal of Computer and Mathematics Education (TURCOMAT). 12 |
| ISSN: | 1309-4653 |
| DOI: | 10.17762/turcomat.v12i2.1898 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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