Special concepts of edge regularity in the cubic fuzzy graph structure environment with an application

Abstract

The cubic fuzzy graph structure is a tool for modeling problems, in which there are two fuzzy values for each variable and the relationships between them that cannot be expressed as a single fuzzy number. Inducing the same relationship among different subjects has an important effect on the understanding of uncertain problems. This is especially ambiguous and complicated when we are dealing with two different fuzzy values. With the aim of explaining edge regular in relationships among vertices, the current research has introduced this concept in the cubic fuzzy graph structure and expressed some of its characteristics. The edge regular and the total edge regularity are described in relation to several relationships. This concept has been applied in some special types such as the complete cubic fuzzy graph structure, and its results have been reviewed. Moreover, the vertex regular and its relationship with the edge regularity have been discussed. This study showed that the degree of vertices is effective in the edge adjustment process. In the end, an application of the topic under discussion is presented.