Parametric Study of Different Classes of Fuzzy Graphs_ Isomorphisms Complements and Regularity

Abstract

Any dissimilar fuzzy graph hypothesis needs large data for training to be able to newlinehelp in decision-making which is crucial to utilitarian research in science and technology. newlineIn this thesis, we introduced strongly regular bipolar fuzzy graph, partially edge regular newlineand fully edge regular bipolar fuzzy graph, p-morphism on interval-valued fuzzy graphs, newlineproduct m-polar fuzzy line graphs, density of a product m-polar fuzzy graphs and some newlineresults were obtained. newlineIn the first chapter, we collected some preliminaries for later use. newlineIn the second chapter, the concepts of edge regular, strongly regular and biregular newlinebipolar fuzzy graphs were introduced. We studied various methods of their newlineconstruction and discussed some of their basic properties. Also, we introduced partially newlineedge regular, fully edge regular bipolar fuzzy graphs and some of their properties were newlinediscussed. newlineIn the third chapter, we introduced the notion of an interval-valued p -morphism newlineon interval-valued fuzzy graphs and highly irregular product interval-valued fuzzy newlinegraphs. First we proved that the relation p -morphism is an equivalence relation in the newlinecollection of interval-valued fuzzy graphs. The actions of interval-valued p -morphism on newlinestrong interval-valued fuzzy graphs were studied. Some theorems on weak and co-weak newlineisomorphism were obtained. Also, and#61549;and#61472;-complement of highly irregular product intervalvalued newlinefuzzy graphs, and#61537;and#61472;-cut and strength cut graphs of an interval-valued fuzzy graphs newlinewere discussed.In the next chapter, we studied the Cartesian product and composition of two mpolar newlinefuzzy graphs and compute the degrees of the vertices in these graphs. newline newline