AUTHOR=Li Li , Kosari Saeed , Sadati Seyed Hossein , Talebi Ali Asghar 

TITLE=Concepts of vertex regularity in cubic fuzzy graph structures with an application

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1087225

DOI=10.3389/fphy.2022.1087225

ISSN=2296-424X

ABSTRACT=A cubic fuzzy graph is a type of fuzzy graph that simultaneously supports fuzzy membership and interval-valued fuzzy membership. This simultaneity leads to better flexibility in modeling problems with respect to uncertain variables. The cubic fuzzy graph structure, as a combination of cubic fuzzy graphs and fuzzy graph structures, shows better capabilities in solving complex problems, especially where there are multiple relationships. This research work has investigated regularity on cubic fuzzy graph structures. In this context, the concepts of vertex regularity and total vertex regularity have been informed and some of its properties have been studied. In this regard, a comparative study between vertex regular and total vertex regular cubic fuzzy graph structure has been carried out and the necessary and sufficient conditions have been provided. These degrees can be easily compared in the form of a cubic number expressed. It has been found that the condition of the membership function is effective in the quality of degree calculation. In the end, an application of the degree of vertices in the cubic fuzzy graph structure is presented.