Summary: 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 \(u\in V-D\), there exists a vertex \(v\in D\) such that \(d(u,v)\geq\deg(u)+\deg(v)\). The minimum cardinality of a dm-set is called the distance majorization number of \(G\) (or dm-number of \(G)\) and is denoted by \(\mathrm{dm}(G)\), 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 \(K_n\), \(K_{1,n}\), \(K_{m,n}\), \(C_n,P_n\), compute bounds on dm-number and dm-number of self complementary graphs and Mycielskian of graphs.