On Alberson irregularity measure of graphs

Abstract

Let G = (V,E), V = {1,2, . . . ,n} be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≥ d2 ≥ ·· · ≥ dn > 0, di = d(i). The irregularity measure of graph is defined as irr(G)=∑i∼ j ∣∣di −d j∣∣, where i∼ j denotes adjacency of vertices i and j. New upper bounds for irr(G) are obtained.