Maker-Breaker domination game played on corona products of graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912754496962560 |
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| author | Divakaran, Athira James, Tijo Klavžar, Sandi Nair, Latha S |
| author_facet | Divakaran, Athira James, Tijo Klavžar, Sandi Nair, Latha S |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maker-Breaker domination game played on corona products of graphs Divakaran, Athira James, Tijo Klavžar, Sandi Nair, Latha S Combinatorics 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. |
| title | Maker-Breaker domination game played on corona products of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.13581 |