Total and paired domination numbers of some wheel-related graphs

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., ۱۳(S) (۲۰۱۹) ۱۱۳--۱۲۱).

کلیدواژه ها:

Total domination numbe ، paired domination number ، wheel graph ، Jahangir graph