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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.14341 |
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| _version_ | 1866915636880343040 |
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| author | Annor, Dickson Y. B. |
| author_facet | Annor, Dickson Y. B. |
| contents | A graph $G$ is a \emph{cover} of a graph $F$ if there exists an onto mapping $π: V(G) \to V(F)$, called a (\emph{covering}) \emph{projection}, such that $π$ maps the neighbours of any vertex $v$ in $G$ bijectively onto the neighbours of $π(v)$ in $F$. This paper is the first attempt to study the connection between domination parameters and graph covers. We focus on the domination number, the total domination number, and the connected domination number. We prove upper and lower bounds for the domination parameters of $G$. Moreover, we propose a conjecture on the lower bound for the domination number of $G$ and provide evidence to support the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Domination Parameters of Graph Covers Annor, Dickson Y. B. Combinatorics 05C69 A graph $G$ is a \emph{cover} of a graph $F$ if there exists an onto mapping $π: V(G) \to V(F)$, called a (\emph{covering}) \emph{projection}, such that $π$ maps the neighbours of any vertex $v$ in $G$ bijectively onto the neighbours of $π(v)$ in $F$. This paper is the first attempt to study the connection between domination parameters and graph covers. We focus on the domination number, the total domination number, and the connected domination number. We prove upper and lower bounds for the domination parameters of $G$. Moreover, we propose a conjecture on the lower bound for the domination number of $G$ and provide evidence to support the conjecture. |
| title | Domination Parameters of Graph Covers |
| topic | Combinatorics 05C69 |
| url | https://arxiv.org/abs/2502.14341 |