English

Maker-Breaker domination game played on corona products of graphs

Combinatorics 2025-12-10 v3

Abstract

In the Maker-Breaker domination game, Dominator and Staller play on a graph GG by taking turns in which each player selects a not yet played vertex of GG. Dominator's goal is to select all the vertices in a dominating set, while Staller aims to prevent this from happening. In this paper, the game is investigated on corona products of graphs. Its outcome is determined as a function of the outcome of the game on the second factor. Staller-Maker-Breaker domination numbers are determined for arbitrary corona products, while Maker-Breaker domination numbers of corona products are bounded from both sides. All the bounds presented are demonstrated to be sharp. Corona products as well as general graphs with small (Staller-)Maker-Breaker domination numbers are described.

Keywords

Cite

@article{arxiv.2402.13581,
  title  = {Maker-Breaker domination game played on corona products of graphs},
  author = {Athira Divakaran and Tijo James and Sandi Klavžar and Latha S Nair},
  journal= {arXiv preprint arXiv:2402.13581},
  year   = {2025}
}