Component Connectivity of Alternating Group Networks and Godan Graphs

Abstract

Connectivity is an important index to evaluate the reliability and fault tolerance of a graph. As a natural extension of the connectivity of graphs, the [Formula: see text]-component connectivity of a graph [Formula: see text], denoted by [Formula: see text], is the minimum number of vertices whose removal from [Formula: see text] results in a disconnected graph with at least [Formula: see text] components. It is a scientific issue to determine the exact values of [Formula: see text] for distinguishing the fault tolerability of networks. However, [Formula: see text]-component connectivity of many well-known interconnection networks has not been explored even for small [Formula: see text]. For the [Formula: see text]-dimensional alternating group networks [Formula: see text] and [Formula: see text]-dimensional godan graphs [Formula: see text], we show that [Formula: see text] for [Formula: see text], and [Formula: see text] for [Formula: see text] and [Formula: see text].