Isomorphism on Complex Fuzzy Graph

Objective: To investigate isomorphism between two complex fuzzy graphs and prove it is an equivalence relation. The major objective of this research paper is to elucidate weak and strong isomorphism, and the study also endeavours to look at the complement of complex fuzzy graphs. Methods: Isomorphism is examined by comparing the membership values of nodes and arcs (both amplitude and phase). The same technique also proves further validation of the equivalence relation, which is also proven by the same technique. This criterion helps us to identify and formalise the isomorphic relationship between complex fuzzy graphs. Findings: This study demonstrates that isomorphism in complex fuzzy graphs allows for consideration of graph structures' differences and similarities. It provides for a better understanding of significant connections between complex fuzzy graphs. Novelty: By offering an elaborate perception of the idea of isomorphism in complex fuzzy graphs, this work advances the discipline. It seeks a better understanding of the complexities of equivalency determination for complicated structures, as well as the application of isomorphism theory to complex fuzzy graphs. Keywords: Complex fuzzy graph, Homomorphism, Isomorphism, Partial order relation, Self complementary