## Abstract

Let H be an arbitrary graph with vertex set V (H) = [n_{H}] = [1, . . . , n_{H}]. The generalized Sierpiński graph S^{n}_{H} , n ∈, is defined on the vertex set [n_{H}]^{n}, two different vertices u = u_{n} . . . u_{1} and v = v_{n} . . . v_{1} being adjacent if there exists an h ∈ [n] such that (a) u_{t} = v_{t}, for t > h, (b) u_{h} ≠ v_{h} and u_{h}v_{h} ∈ E(H), and (c) u_{t} = v_{h} and v_{t} = u_{h} for t < h. If H is the complete graph K_{k}, then we speak of the Sierpiński graph S^{n}_{k}. We present an algorithm that recognizes Sierpiński graphs S^{n}_{k} in O(|V (S^{n}_{k})|1+1/^{n}) = O(|E(S^{n}_{k})|) time. For generalized Sierpiński graphs S^{n}_{H} 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 S^{n}_{H}.

Original language | English |
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Pages (from-to) | 122-137 |

Number of pages | 16 |

Journal | Applicable Analysis and Discrete Mathematics |

Volume | 14 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Apr 2020 |

Externally published | Yes |

## Keywords

- Algorithm
- Generalized sierpiński graphs
- Sierpiński graphs

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics