Affiliations:
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
Correspondence:
[*]
Corresponding author. ZengTai Gong, College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. Tel.: +86 09317971430. E-mails: [email protected]; [email protected].
Note: [1] This work is supported by the National Natural Science Foundation of China (Grant No.12061067).
Abstract: 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.
Keywords: Cycle connectivity, intuitionistic fuzzy graphs, cyclic connectivity index
