γ-induced-paired dominating graphs of paths and cycles

Abstract

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

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

“…They studied T D γ (P k ) and T D γ (C k ). The γ-independent dominating graph [19] and the γ-induced-paired dominating graph [20] are defined similarly.…”