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Maximal outerplanar graphs with semipaired domination number double the domination number | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 11، شماره 1، خرداد 2026، صفحه 1-20 اصل مقاله (1.85 M) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28972.1801 | ||
| نویسندگان | ||
| Michael A. Henning1؛ Pawaton Kaemawichanurat* 2، 3 | ||
| 1Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, 2006 South Africa | ||
| 2Mathematics and Statistics with Applications (MaSA) | ||
| 3Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand | ||
| چکیده | ||
| A subset $S$ of vertices in a graph $G$ is a dominating set if every vertex in $V(G) \setminus S$ is adjacent to a vertex in $S$. If the graph $G$ has no isolated vertex, then a pair dominating set $S$ of $G$ is a dominating set of $G$ such that $G[S]$ has a perfect matching. Further, a semipaired dominating set of $G$ is a dominating set of $G$ with the additional property that the set $S$ can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set of $G$. Similarly, the paired (semipaired) domination number $\gamma_{pr}(G)$ $(\gamma_{pr2}(G))$ is the minimum cardinality of a paired (semipaired) dominating set of $G$. It is known that for a graph $G$, $\gamma(G) \le \gamma_{pr2}(G) \le \gamma_{pr}(G) \le 2\gamma(G)$. In this paper, we characterize maximal outerplanar graphs $G$ satisfying $\gamma_{pr2}(G) = 2\gamma(G)$. Hence, our result yields the characterization of maximal outerplanar graphs $G$ satisfying $\gamma_{pr}(G) = 2\gamma(G)$. | ||
| کلیدواژهها | ||
| paired-domination؛ semipaired domination number؛ maximal outerplanar graphs | ||
| مراجع | ||
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