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

• DOI: 10.3389/fphy.2022.1087225
• Publication Date: 2023-04-20T19:58:55Z
• Authors: Li Li; Saeed Kosari; Seyed Hossein Sadati; Ali Asghar Talebi
• Keywords: Physics; QC1-999; 0202 electrical engineering, electronic engineering, information engineering; ℬi-vertex regularity; total ℬi-vertex regularity; cubic fuzzy graph structure; 0101 mathematics; ℬi-degree; total ℬi-degree; perfectly ℬi-vertex regular

The cubic fuzzy graph structure, as a combination of cubic fuzzy graphs and fuzzy graph structures, shows better capabilities in solving complex problems, especially in cases where there are multiple relationships. The quality and method of determining the degree of vertices in this type of fuzzy graphs simultaneously supports fuzzy membership and interval-valued fuzzy membership, in addition to the multiplicity of relations, motivated us to conduct a study on the regularity of 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.