On the minimum cut-sets of the power graph of a finite cyclic group

Abstract

The power graph [Formula: see text] of a finite group [Formula: see text] is the simple graph with vertex set [Formula: see text], in which two distinct vertices are adjacent if one of them is a power of the other. For an integer [Formula: see text], let [Formula: see text] denote the cyclic group of order [Formula: see text] and let [Formula: see text] be the number of distinct prime divisors of [Formula: see text]. For [Formula: see text], the minimum cut-sets of [Formula: see text] are characterized in [S. Chattopadhyay, K. L. Patra and B. K. Sahoo, Vertex connectivity of the power graph of a finite cyclic group, Discrete Appl. Math. 266 (2019) 259–271]. In this paper, for [Formula: see text], we identify certain cut-sets of [Formula: see text] such that any minimum cut-set of [Formula: see text] must be one of them.