Movable Independent Dominating Sets in Paths and Cycles

Abstract

A nonempty set S ⊆ V (G) is a 1-movable independent dominating set of G if S is an independent dominating set of G and for every v ∈ S,there exists a vertex u ∈ (V (G)\S)∩NG(v) such that (S\{v})∪{u} is an independent dominating set of G.The 1-movable independent domination number of G denoted by γmi 1 (G) is the smallest cardinality of a 1-movable independent dominating of G. This paper characterizes 1-movable independent dominating sets in a path Pn and a cycle Cn.