## Abstract

Let G and H be graphs and let f: V(G) → V(H) be a function. The Sierpiński product of G and H with respect to f, denoted by G⊗ _{f}H , is defined as the graph on the vertex set V(G) × V(H) , consisting of |V(G)| copies of H; for every edge gg^{′} of G there is an edge between copies gH and g^{′}H of H associated with the vertices g and g^{′} of G, respectively, of the form (g, f(g^{′})) (g^{′}, f(g)) . The Sierpiński metric dimension and the upper Sierpiński metric dimension of two graphs are determined. Closed formulas are determined for Sierpiński products of trees, and for Sierpiński products of two cycles where the second factor is a triangle. We also prove that the layers with respect to the second factor in a Sierpiński product graph are convex.

Original language | English |
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Article number | 3 |

Journal | Mediterranean Journal of Mathematics |

Volume | 21 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2024 |

## Keywords

- Sierpiński product of graphs
- convex subgraph
- metric dimension
- tree

## ASJC Scopus subject areas

- General Mathematics