Ali Ghalavand - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan ۸۷۳۱۷-۵۳۱۵۳, I. R. Iran
Ali Reza Ashrafi - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan ۸۷۳۱۷-۵۳۱۵۳, I. R. Iran

Let $G$ be an $n-$vertex graph with $m$ vertices‎. ‎The degree deviation measure of $G$ is defined as‎ ‎$s(G)$ $=$ $\sum_{v\in V(G)}|deg_G(v)‎- ‎\frac{۲m}{n}|,$ where $n$ and $m$ are the number of vertices and edges of $G$‎, ‎respectively‎. ‎The aim of this paper is to prove the Conjecture ۴.۲ of [J‎. ‎A‎. ‎de Oliveira‎, ‎C‎. ‎S‎. ‎Oliveira‎, ‎C‎. ‎Justel and N‎. ‎M‎. ‎Maia de Abreu‎, ‎Measures of irregularity of graphs‎, Pesq‎. ‎Oper.‎, ‎۳۳ (۲۰۱۳) ۳۸۳--۳۹۸]‎. ‎The degree deviation measure of chemical graphs under some conditions on the cyclomatic number is also computed‎.

‎irregularity‎, ‎degree deviation measure‎, ‎chemical graph