A connectivity index based on adjacent vertices in cubic fuzzy graph with an application

Abstract

A cubic fuzzy graph is a type of fuzzy graph that simultaneously supports two different fuzzy memberships. The study of connectivity in cubic fuzzy graph is an interesting and challenging topic. This research generalized the neighborhood connectivity index in a cubic fuzzy graph with the aim of investigating the connection status of nodes with respect to adjacent vertices. In this survey, the neighborhood connectivity index was introduced in the form of two numerical and distance values. Some characteristics of the neighborhood connectivity index were investigated in cubic fuzzy cycles, saturated cubic fuzzy cycle, complete cubic fuzzy graph and complementary cubic fuzzy graph. The method of constructing a cubic fuzzy graph with arbitrary neighborhood connectivity index was the other point in this research. The results showed that the neighborhood connectivity index depends on the potential of nodes and the number of neighboring nodes. This research was conducted on the Central Bank’s data regarding inter-bank relations and its results were compared in terms of neighborhood connectivity index.