Path center of a fuzzy graph based on µ-distance

Abstract

Graph theory has put forward a mathematical foundation for modelling and fine tuning communication and transportation networks. Centers and path centers serve as effective tools for optimizing traffic flow and efficiently allocating resources. The present article examines the concepts of eccentricity, center and path center of a fuzzy graph based on µ-distance. The major contribution of this article is an algorithm to find the path center and center of trees in fuzzy context. Many characteristics of center and path center of fuzzy graphs are explored and illustrated. Furthermore, eccentricities of adjacent nodes in a fuzzy graph and eccentricities of end nodes of effective arcs and strongly µ-related nodes are investigated.