On a Conjecture about Degree Deviation Measure of Graphs

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.

کلیدواژه ها:

‎irregularity‎ ، ‎degree deviation measure‎ ، ‎chemical graph