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 < h. If H is the complete graph Kk, then we speak of the Sierpiński graph Snk. We present an algorithm that recognizes Sierpiński graphs Snk in O(|V (Snk)|1+1/n) = O(|E(Snk)|) time. For generalized Sierpiński graphs SnH we present a polynomial time algorithm for the case when H belong to a certain well defined class of graphs. We also describe how to derive the base graph H from an arbitrarily given SnH.
- Generalized sierpiński graphs
- Sierpiński graphs
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics