On a Conjecture about Degree Deviation Measure of Graphs

Document Type: Research Paper

Authors

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran

10.22108/toc.2020.121737.1709

Abstract

Let $G$ be an $n-$vertex graph with $m$ vertices‎. ‎The degree deviation measure of $G$ is defined as‎ ‎$s(G)$ $=$ $\sum_{v\in V(G)}|deg_G(v)‎- ‎\frac{2m}{n}|,$ 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, ‎\emph{Pesq‎. ‎Oper.}, \textbf{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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