Total and paired domination numbers of some wheel-related graphs

Eakawinrujee, Pannawat; Trakultraipruk, Nantapath

doi:10.22108/toc.2025.145488.2286

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	Total and paired domination numbers of some wheel-related graphs
Transactions on Combinatorics
دوره 15، شماره 4، اسفند 2026، صفحه 251-272 اصل مقاله (523.11 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.145488.2286
نویسندگان
Pannawat Eakawinrujee¹؛ Nantapath Trakultraipruk^* ²
¹Thammasat Secondary School, Faculty of Learning Sciences and Education, Thammasat University, Pathum Thani 12120, Thailand
²Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand
چکیده
Let $G$ be a graph without isolated vertices. A total dominating set of $G$ is a set $D\subseteq V(G)$ such that every vertex of $G$ is adjacent to some vertex in $D$. A paired dominating set of $G$ is a total dominating set whose induced subgraph has a perfect matching. The total (paired) domination number of $G$ is the minimum cardinality of a total (paired) dominating set of $G$. In this paper, we determine the total and the paired domination numbers of some wheel-related graphs. We also give upper bounds on the total and the paired domination numbers of closed helm graphs and web graphs. Moreover, we determine the paired domination numbers of Jahangir graphs and correct some results on the total domination numbers presented by Mtarneh et al. (Malays. J. Math. Sci., 13(S) (2019) 113--121).
کلیدواژه‌ها
Total domination numbe؛ paired domination number؛ wheel graph؛ Jahangir graph

مراجع
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Total and paired domination numbers of some wheel-related graphs