{"title":"关于图度偏差测度的一个猜想","authors":"A. Ghalavand, A. Ashrafi","doi":"10.22108/TOC.2020.121737.1709","DOIUrl":null,"url":null,"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.","PeriodicalId":8442,"journal":{"name":"arXiv: Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On a Conjecture about Degree Deviation Measure of Graphs\",\"authors\":\"A. Ghalavand, A. Ashrafi\",\"doi\":\"10.22108/TOC.2020.121737.1709\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":8442,\"journal\":{\"name\":\"arXiv: Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2020.121737.1709\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2020.121737.1709","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
设G是一个有m条边的n顶点图。G的度偏差度量定义为s(G)=sum v in v (G)|degG(v)-(2m/n)|，其中n为G的顶点数，m为G的边数。本文的目的是证明J A de Oliveira, C S Oliveira, C Justel和N M Maia de Abreu的猜想4.2，图的不规则性度量，Pesq。卷33(3)(2013)383-398]。计算了化学图在一定条件下对圈数的度偏差测度。
On a Conjecture about Degree Deviation Measure of Graphs
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.
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