F-Paired Dominating Graphs of Some Paths and Some Cycles

A set D of vertices in a graph G is a paired dominating set of G if every vertex of G is adjacent to some vertex in D and the subgraph of G induced by D contains a perfect matching. The maximum cardinality of a minimal paired dominating set of G is called the upper paired domination number, denoted by Fpr(G). A minimal paired dominating set with cardinality Fpr(G) is a Fpr(G)-set. The F-paired dominating graph PDr(G) of G is the graph whose vertices are Fpr(G)-sets and any two Fpr(G)-sets are adjacent in PDr(G) if they differ by exactly one vertex. In this paper, we first correct some results on the F-paired dominating graphs of some paths that appeared in [P. Eakawinrujee, N. Trakultraipruk, F-paired dominating graphs of some paths, MATEC Web Conf. 189 (2018) 03029] and then we determine the F-paired dominating graphs of some cycles.