Total and paired domination numbers of windmill graphs
Pannawat Eakawinrujee, Nantapath Trakultraipruk · Asian-European Journal of Mathematics · 2023
Let [Formula: see text] be a graph without isolated vertices. A total dominating set of [Formula: see text] is a set [Formula: see text] of vertices of [Formula: see text] such that every vertex of [Formula: see text] is adjacent to at least one vertex in [Formula: see text]. A total dominating set [Formula: see text] is a paired dominating set of [Formula: see text] if the subgraph of [Formula: see text] induced by [Formula: see text] has a perfect matching. The minimum cardinality of a total dominating set (respectively, a paired dominating set) is called the total domination number (respectively, the paired domination number). This paper determines the total domination numbers and the paired domination numbers of windmill graphs.