An analysis on (([rα, rβ], rγ), 2,([kα, kβ], kγ)) – regular and total regular cubic fuzzy graphs

Abstract

This article introduces the concepts of (([rα, rβ], rγ), 2,([kα, kβ], kγ)) - regular and total (([rα, rβ], rγ), 2,([kα, kβ], kγ)) - regular cubic fuzzy graphs, extending fuzzy graph theory by applying regularity conditions to both vertex and edge membership functions. The study defines and analyzes the vertex d2 - degree and Total d2 – degree in cubic fuzzy graphs, including (([rα, rβ], rγ), 2,([kα, kβ], kγ)) - regularity and Total (([rα, rβ], rγ), 2,([kα, kβ], kγ)) - regularity to determine the conditions under which a cubic fuzzy graph is regular. Furthermore, (([rα, rβ], rγ), 2,([kα, kβ], kγ)) - regularity is examined in cyclic cubic fuzzy graphs with specific membership values. Our results formalize new regularity conditions in cubic fuzzy graphs, providing a deeper understanding of their properties. The study further explores the regularity properties of cubic fuzzy graphs, providing new tools for potential applications in fields such as network analysis, decision-making and related fields.