Inverse [1, 2] – Domination in Graphs

Author(s): Sathish. T, Padma Priya. C

Abstract: A vertex subset S of a Graph G = {V, E} is an inverse [1, 2] – dominating set if, 1≤| N(v) ∩ S′ |≤ 2, for every vertex v∈V-S’ (i. e) each vertex v∈V-S’ is adjacent to atleast 1 or 2 vertices in S′. In other way, the distance between any two vertices in V – S′ is either 1 or 2 for any vertex set in S′. The lowest cardinality of an inverse [1, 2]-dominating set of graph G is called an inverse [1, 2]-domination number of G and is denoted by γ′[1, 2](G). In this paper, we extract the perfect values of γ′[1, 2](G) for few standard graphs and additionally, we use the general results to illustrate the interrelation between γ′[1, 2](G) and other criterions.