Cycle connectivity and cyclic connectivity index of intuitionistic fuzzy graphs1

Connectivity parameters play a crucial role in network analysis. The cyclic reachability is an important attribute that determines the connectivity of the network, the strength of the cycles in intuitionistic fuzzy graphs (IFGs) is not unique. This article first introduces several concepts of cycle connectivity of IFGs, and then discusses the related properties. On the basis of the cycle connectivity of IFGs, the concepts of cyclic connectivity index (CCI) and average cyclic connectivity index (ACCI) are proposed, which can be used to express the reachability of cycle. Some results of CCI on IFGs are discussed, such as cutvertices, trees, and complete intuitionistic fuzzy graphs. The vertices of IFGs are divided into three categories according to ACCI. Two algorithms are introduced, one to find CCI and ACCI of a given IFGs and the other to identify the nature of vertices.