γ-Paired dominating graphs of lollipop, umbrella and coconut graphs

Pannawat Eakawinrujee (Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand)
Nantapath Trakultraipruk (Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications

A paired dominating set of a graph G is a dominating set whose induced subgraph has a perfect matching. The paired domination number γpr(G) of G is the minimum cardinality of a paired dominating set. A paired dominating set D is a γpr(G)-set if |D|=γpr(G). The γ-paired dominating graph PDγ(G) of G is the graph whose vertex set is the set of all γpr(G)-sets, and two γpr(G)-sets D1 and D2 are adjacent in PDγ(G) if D2 = (D1 \ {u}) ∪ {v} for some u ∈ D1 and v ∉ D1. This paper determines the paired domination numbers of lollipop graphs, umbrella graphs, and coconut graphs. We also consider the γ-paired dominating graphs of those three graphs.