Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completen...

Polar graphs generalise bipartite graphs, cobipartite graphs, and split graphs, and they constitute a special type of matrix partitions. A graph is polar if its vertex set can be partitioned into two, such that one part induces a complete multipartite graph and the other part induces a disjoint union of complete graphs. Deciding whether a given arbitrary graph is polar, is an NP-complete proble...

A fuzzy graph can be obtained from two given fuzzy graphs using union and join. In this paper, we find the degree of an edge in fuzzy graphs formed by these operations in terms of the degree of edges in the given fuzzy graphs in some particular cases. 1. Introduction Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975 [4]. Though it is very young, it has been growing fast and has nume...

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

In this article, we introduce some connectivity concepts in bipolar fuzzy graphs. Analogous to fuzzy cutvertices and fuzzy bridges in fuzzy graphs, bipolar fuzzy cutvertices and bipolar fuzzy bridges are introduced and characterized. We also propose the concepts of gain and loss for paths and pairs of vertices. Connectivity in complete bipolar fuzzy graphs is also discussed.