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arXiv · 2402.13581

Maker-Breaker domination game played on corona products of graphs

Athira Divakaran·Tijo James·Sandi Klavžar·Latha S Nair
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Abstract

In the Maker-Breaker domination game, Dominator and Staller play on a graph $G$ by taking turns in which each player selects a not yet played vertex of $G$. 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.

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Athira Divakaran, Tijo James, Sandi Klavžar, Latha S Nair. 2024-02-21. Maker-Breaker domination game played on corona products of graphs. https://doi.org/10.2989/16073606.2024.2412835

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