1-movable Perfect Domination in Graphs - Lomarda-Hinampas, Jocecar (Journal of Global Research in Mathematical Archives(JGRMA), 2018)
A nonempty subset S of V (G) is a 1-movable perfect dominating set of G if S = V (G) or S ⊂ V (G) is a perfect dominating set of G and for every v ∈ S, there exists u ∈ (V (G) \ S) ∩ NG(v) such that (S \ {v}) ∪ {u} is a perfect dominating set of G. The smallest cardinality of a 1-movable perfect dominating set of G is called 1-movable perfect domination number of G, denoted by γmp 1 (G). A 1-movable perfect dominating set of G with cardinality equal to γmp 1 (G) is called γmp 1 -set of G. This paper characterizes of the 1-movable perfect dominating sets in the join and corona of two connected graphs