On the Extra Connectivity of the Power Graph of a Finite Cyclic Group

Abstract

Reliability evaluation of an interconnection network is of great significance for construction and maintenance of the network. The extra connectivity and essentially edge-connectivity are two important parameters to evaluate network reliability. Let [Formula: see text] be a finite group. The power graph [Formula: see text] of [Formula: see text] is defined as an undirected graph whose vertex set is [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if one is a power of the other. In this paper, we determine the [Formula: see text]-extra connectivity and essentially edge-connectivity of the power graph of a cyclic finite group.