Recognizing generalized sierpiński graphs

Wilfried Imrich, Iztok Peterin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)122-137
Number of pages16
JournalApplicable Analysis and Discrete Mathematics
Issue number1
Publication statusPublished - 1 Apr 2020
Externally publishedYes


  • Algorithm
  • Generalized sierpiński graphs
  • Sierpiński graphs

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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