Equitable restrained domination number of some graphs

Abstract

A dominating set S ⊆ V is said to be a restrained dominating set of graph G if every vertex not in S is adjacent to a vertex in S and also to a vertex in V − S. A set S ⊆ V is called an equitable dominating set if for every vertex v ∈ V −S, there exist a vertex u ∈ S such that uv ∈ E and |deg(u)−deg(v)| ≤ 1. A dominating set S is called an equitable restrained dominating set if it is both restrained and equitable. The minimum cardinality of an equitable restrained dominating set is called equitable restrained domination number of G, denoted by γ e r (G). We investigate γ e r (G) parameter for some standard graphs and also establish some characterizations.