On a Conjecture about Degree Deviation Measure of Graphs

Abstract

Let G be an n−vertex graph with m edges. The degree deviation measure of G is defined as swhere n and m are the number of vertices and edges of G, respectively. The aim of this paper is to prove the Conjecture 4.2 of [J. A. de Oliveira, C. S. Oliveira, C. Justel and N. M. Maia de Abreu, Measures of irregularity of graphs, Pesq. Oper. 33 (3) (2013) 383-398]. The degree deviation measure of chemical graphs under some conditions on the cyclomatic number is also computed.