3-Path-Connectivity of Cayley Graphs Generated by Wheel Graphs

Let [Formula: see text] be a simple connected graph and [Formula: see text] a subset of [Formula: see text] with [Formula: see text]. An [Formula: see text]-path in [Formula: see text] is a path that connects all vertices of [Formula: see text]. Two [Formula: see text]-paths [Formula: see text] and [Formula: see text] are said to be internally disjoint if [Formula: see text] and [Formula: see text]. Denote by [Formula: see text] the maximum number of internally disjoint [Formula: see text]-paths in [Formula: see text]. For an integer [Formula: see text], the [Formula: see text]-path-connectivity [Formula: see text] of [Formula: see text] is defined as [Formula: see text] and [Formula: see text]. Let [Formula: see text] denote the Cayley graph generated by the [Formula: see text]-vertex wheel graph. In this paper, we investigate the 3-path-connectivity of [Formula: see text] and prove that [Formula: see text] for all [Formula: see text].