On Topological Indices of Fuzzy Random Graph

• Published in: Indian journal of science and technology 2024-08, Vol.17 (30), p.3080-3092
• Main Authors: Sarala, N, Abirami, R
• Format: Article
• Language: English
• ISSN: 0974-6846; 0974-5645
• DOI: 10.17485/IJST/v17i30.1695

Objectives: Fuzzy random graphs model uncertain relationships between entities, where edges possess degrees of membership rather than binary connections. This study aims to discover how operations such as union and intersection relate to each other on the topological indices of fuzzy random graphs. By analyzing the topological indices of fuzzy random graphs, our aim is to uncover meaningful insights into the connectivity, complexity and other topological features of fuzzy random graphs. Method: The topological indices of fuzzy random graphs were determined by merging the fuzzy and random graph indices and applying them to the corresponding edges. Findings: This study investigates various topological indices, such as the Connectivity index, the Wiener index, the Zagreb indices, the Harmonic index and the Randić index, adapted to account for the fuzzy nature of graph edges. Novelty: In this work, the topological indices of a particular fuzzy random graph are also examined, and the results are presented. Furthermore, an example-based description of the relationship between operations on the topological indices of fuzzy random graphs is provided. This study describes how topological indices of fuzzy random graphs can be used to locate electric charging stations, predict protein structure and more. Keywords: Fuzzy graph, Random graph, Fuzzy random graph, Degree of Vertices, Topological indices