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Domination parameters of graph covers | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 12، شماره 1، خرداد 2027، صفحه 33-43 اصل مقاله (396.17 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30385.2446 | ||
| نویسنده | ||
| Dickson Y.B. Annor* | ||
| Department of Mathematical and Physical Sciences, La Trobe University, Bendigo, Australia | ||
| چکیده | ||
| A graph $G$ is a \emph{cover} of a graph $F$ if there exists an onto mapping $\pi : V(G) \to V(F)$, called a (\emph{covering}) \emph{projection}, such that $\pi$ maps the neighbours of any vertex $v$ in $G$ bijectively onto the neighbours of $\pi(v)$ 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. | ||
| کلیدواژهها | ||
| domination؛ total domination؛ connected domination؛ graph cover | ||
| مراجع | ||
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