AN ANALYSIS ON (([rα, rβ], rγ), 2, ([kα, kβ], kγ)) – REGULAR AND TOTAL REGULAR CUBIC FUZZY GRAPHS

AN ANALYSIS ON (([rα, rβ], rγ), 2, ([kα, kβ], kγ)) – REGULAR AND TOTAL REGULAR CUBIC FUZZY GRAPHS

J. Befija Minnie, L. Ancy Lara, D. Ajay

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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.

Keywords

Degree of a vertex in Fuzzy Graphs, Total degree of a vertex in Fuzzy Graphs, Regular Fuzzy Graphs, Total Regular Fuzzy Graphs, Cubic Fuzzy Graphs.