Title of article :
On a Conjecture about Degree Deviation Measure of Graphs
Author/Authors :
Ghalavand, Ali Department of Pure Mathematics - Faculty of Mathematical Sciences - University of Kashan, Kashan, I. R. Iran , Ashrafi, Ali Reza Department of Pure Mathematics - Faculty of Mathematical Sciences - University of Kashan, Kashan, I. R. Iran
Abstract :
Let G be an n−vertex graph with m vertices. The degree deviation measure of G is defined as s(G) = ∑v∈V(G)|degG(v)−2mn|, 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.
Keywords :
irregularity , degree deviation measure , chemical graph
Journal title :
Transactions on Combinatorics
