Strong equitable and inverse strong equitable domination number of some special classes of graphs

Abstract

Let G = (V, E) be a simple, finite, undirected and connected graph. A non-empty subset D of V(G) is called a strong equitable dominating set of G if for every v V-D, there exists atleast one u D such that u and v are adjacent, also deg (u) ≥ deg (v) and if for every v V-D, there exists a vertex u D such that uv E(G) and ≤1. The minimum cardinality of such a minimal strong equitable dominating set is called a strong equitable domination number and it is denoted by se(G).If is a strong equitable dominating set, then is called an inverse strong equitable dominating set. The minimum cardinality of a minimal inverse strong equitable dominating set is called an inverse strong equitable domination number and it is denoted by