On a Conjecture about Degree Deviation Measure of Graphs
Combinatorics
2020-02-24 v1
Abstract
Let G be an n-vertex graph with m edges. The degree deviation measure of G is defined as s(G)=sum v in V(G)|degG(v)-(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 (3) (2013) 383-398]. The degree deviation measure of chemical graphs under some conditions on the cyclomatic number is also computed.
Keywords
Cite
@article{arxiv.2002.09020,
title = {On a Conjecture about Degree Deviation Measure of Graphs},
author = {Ali Ghalavand and Ali Reza Ashrafi},
journal= {arXiv preprint arXiv:2002.09020},
year = {2020}
}