Total and paired domination numbers of some wheel-related graphs

Document Type : Research Paper

Authors

1 Thammasat Secondary School, Faculty of Learning Sciences and Education, Thammasat University, Pathum Thani 12120, Thailand

2 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand

Abstract

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).

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Main Subjects

References

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Transactions on Combinatorics
Volume 15, Issue 4 - Serial Number 4
December 2026
Pages 251-272

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History

  • Receive Date: 31 May 2025
  • Revise Date: 18 November 2025
  • Accept Date: 15 November 2025
  • Published Online: 29 November 2025

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