Recognizing generalized sierpiński graphs

Abstract

Let H be an arbitrary graph with vertex set V (H) = [nH] = [1, . . . , nH]. The generalized Sierpiński graph SnH , n ∈, is defined on the vertex set [nH]n, two different vertices u = un . . . u1 and v = vn . . . v1 being adjacent if there exists an h ∈ [n] such that (a) ut = vt, for t > h, (b) uh ≠ vh and uhvh ∈ E(H), and (c) ut = vh and vt = uh for t