Independence complexes of power graphs of cyclic groups of order pnqm

The power graph [Formula: see text] of a group [Formula: see text] is the simple and undirected graph with vertex set [Formula: see text] and with two distinct vertices being adjacent, whenever one of them is a positive power of the other in [Formula: see text]. The independence complex of a graph [Formula: see text], is the simplicial complex [Formula: see text] with the vertex set being that of [Formula: see text] and the simplices being the independent sets of [Formula: see text]. In this paper, we study the homotopy type of the independence complex of power graphs of cyclic groups of order [Formula: see text], where [Formula: see text] and [Formula: see text] are distinct primes and [Formula: see text].