特征度的二部除数图

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2017-03-01 DOI:10.22108/IJGT.2017.9852

S. A. Moosavi

{"title":"特征度的二部除数图","authors":"S. A. Moosavi","doi":"10.22108/IJGT.2017.9852","DOIUrl":null,"url":null,"abstract":"‎‎The concept of the bipartite divisor graph for integer subsets has been considered in [M‎. ‎A‎. ‎Iranmanesh and C‎. ‎E‎. ‎Praeger‎, ‎Bipartite divisor graphs for integer subsets‎, Graphs Combin.‎, 26 (2010) 95--105.]‎. ‎In this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $G$ and obtain some properties of this graph‎. ‎We show that if $G$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $G$ is a non-solvable group‎, ‎then it has at most $3$ connected components‎. ‎We also show that‎ ‎the diameter of a connected bipartite divisor graph is bounded by $7$ and obtain some properties of groups whose graphs are complete bipartite graphs‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On bipartite divisor graph for character degrees\",\"authors\":\"S. A. Moosavi\",\"doi\":\"10.22108/IJGT.2017.9852\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"‎‎The concept of the bipartite divisor graph for integer subsets has been considered in [M‎. ‎A‎. ‎Iranmanesh and C‎. ‎E‎. ‎Praeger‎, ‎Bipartite divisor graphs for integer subsets‎, Graphs Combin.‎, 26 (2010) 95--105.]‎. ‎In this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $G$ and obtain some properties of this graph‎. ‎We show that if $G$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $G$ is a non-solvable group‎, ‎then it has at most $3$ connected components‎. ‎We also show that‎ ‎the diameter of a connected bipartite divisor graph is bounded by $7$ and obtain some properties of groups whose graphs are complete bipartite graphs‎.\",\"PeriodicalId\":43007,\"journal\":{\"name\":\"International Journal of Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2017-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/IJGT.2017.9852\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/IJGT.2017.9852","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

[M]讨论了整数子集的二部除数图的概念。‎‎。伊朗和C。‎‎。Praeger，整数子集的二部除数图，图组合。[j]， 26(2010) 95—105。在本文中，我们将考虑有限群$G$的特征度集的图，并得到该图的一些性质。我们证明了如果$G$是一个可解群，那么这个图的连通分量的个数最多为$2，如果$G$是一个不可解群，那么它的连通分量的个数最多为$3。我们还证明了连通二部除数图的直径以7为界，并得到了图为完全二部图的群的一些性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On bipartite divisor graph for character degrees

‎‎The concept of the bipartite divisor graph for integer subsets has been considered in [M‎. ‎A‎. ‎Iranmanesh and C‎. ‎E‎. ‎Praeger‎, ‎Bipartite divisor graphs for integer subsets‎, Graphs Combin.‎, 26 (2010) 95--105.]‎. ‎In this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $G$ and obtain some properties of this graph‎. ‎We show that if $G$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $G$ is a non-solvable group‎, ‎then it has at most $3$ connected components‎. ‎We also show that‎ ‎the diameter of a connected bipartite divisor graph is bounded by $7$ and obtain some properties of groups whose graphs are complete bipartite graphs‎.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.