Abstract
Let $G$ be an $n-$vertex graph with $m$ vertices. The degree deviation measure of $G$ is defined as $s(G)$ $=$ $sum_{vin V(G)}|deg_G(v)- frac{2m}{n}|,$ where $n$ and $m$ are the number of vertices and edges of $G$, respectively. The aim of this paper is to prove the Conjecture 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 (2013) 383--398]. The degree deviation measure of chemical graphs under some conditions on the cyclomatic number is also computed.
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