On a conjecture about degree deviation measure of graphs
نویسندگان
1 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran
2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran
doi
10.22108/toc.2020.121737.1709چکیده
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, Pesq. Oper., 33 (2013) 383--398]. The degree deviation measure of chemical graphs under some conditions on the cyclomatic number is also computed.
