γ-Paired dominating graphs of lollipop, umbrella and coconut graphs - Pannawat Eakawinrujee; Nantapath Trakultraipruk (Electronic Journal of Graph Theory and Applications (EJGTA), 2023)
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.