Distance Majorization Sets in Graphs

Abstract

Let G = V, E be a simple graph. A subset D of V G is said to be a distance majorization set or dm - set if for every vertex u ∈ V − D, there exists a vertex v ∈ D such that d u, v ≥ deg u + deg v . The minimum cardinality of a dm - set is called the distance majorization number of G or dm - number of G and is denoted by dm G , Since the vertex set of G is a dm - set, the existence of a dm - set in any graph is guaranteed. In this paper, we find the dm - number of standard graphs like Kn, K1,n, Km,n, Cn, Pn, compute bounds on dm− number and dm- number of self complementary graphs and mycielskian of graphs.