γ-induced-paired dominating graphs of paths and cycles

For any graph G = (V (G), E(G)), a nonempty subset D of V(G) is called an induced-paired dominating set if every vertex in V (G) is adjacent to some vertex in D, and the induced subgraph G[D] contains only independent edges. An induced-paired dominating set of G with minimum number of vertices is also called a gamma(ip) (G)-set. We define the gamma-induced paired dominating graph of G, denoted by IPD gamma(G), to be the graph whose vertex set, consists of all gamma(ip) (G)-sets, and two gamma(ip )(G)-sets are adjacent, in IPD gamma (G) if they are different from each other by only one vertex. In this paper, we exhibit all gamma-induced-paired dominating graphs of paths and cycles.