Abstract
The notion of a fuzzy graph was initially introduced by Kauffman (Introduction to the theory of fuzzy sets, Academic Press Inc., Orlando) in [91]. However, the development of fuzzy graph theory is due to the ground setting papers of Rosenfeld (Fuzzy sets and their applications, Academic Press, New York) [154] and Yeh and Bang (Fuzzy sets and their applications, Academic Press, New York) [186]. In Rosenfeld’s paper, basic structural and connectivity concepts were presented while Yeh and Bang introduced different connectivity parameters and discussed their application. Rosenfeld obtained the fuzzy analogs of several graph-theoretic concepts like bridges, paths, cycles, trees, and connectedness. Most of the theoretical development of fuzzy graph theory is based on Rosenfeld’s initial work.