关于特殊符号图的注释

Ars Math. Contemp. Pub Date : 2020-09-24 DOI:10.26493/1855-3974.1933.2DF

Z. Stanić

{"title":"关于特殊符号图的注释","authors":"Z. Stanić","doi":"10.26493/1855-3974.1933.2DF","DOIUrl":null,"url":null,"abstract":"A connected signed graph is called exceptional if it has a representation in the root system E 8 , but has not in any D k . In this study we obtain some properties of these signed graphs, mostly expressed in terms of those that are maximal with a fixed number of eigenvalues distinct from −2 . As an application, we characterize exceptional signed graphs with exactly 2 eigenvalues. In some particular cases, we prove the (non-)existence of such signed graphs.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"29 1","pages":"105-115"},"PeriodicalIF":0.0000,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Notes on exceptional signed graphs\",\"authors\":\"Z. Stanić\",\"doi\":\"10.26493/1855-3974.1933.2DF\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A connected signed graph is called exceptional if it has a representation in the root system E 8 , but has not in any D k . In this study we obtain some properties of these signed graphs, mostly expressed in terms of those that are maximal with a fixed number of eigenvalues distinct from −2 . As an application, we characterize exceptional signed graphs with exactly 2 eigenvalues. In some particular cases, we prove the (non-)existence of such signed graphs.\",\"PeriodicalId\":8402,\"journal\":{\"name\":\"Ars Math. Contemp.\",\"volume\":\"29 1\",\"pages\":\"105-115\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ars Math. Contemp.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/1855-3974.1933.2DF\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ars Math. Contemp.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/1855-3974.1933.2DF","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 6

摘要

如果一个连通的有符号图在根e8中有表示，但在任何dk中没有表示，则称为例外图。在这个研究中，我们得到了这些符号图的一些性质，主要是用那些具有固定数目的特征值不同于- 2的极大值来表示的。作为一个应用，我们刻画了恰好有2个特征值的例外符号图。在某些特殊情况下，我们证明了这种符号图的(不)存在性。

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

Notes on exceptional signed graphs

A connected signed graph is called exceptional if it has a representation in the root system E 8 , but has not in any D k . In this study we obtain some properties of these signed graphs, mostly expressed in terms of those that are maximal with a fixed number of eigenvalues distinct from −2 . As an application, we characterize exceptional signed graphs with exactly 2 eigenvalues. In some particular cases, we prove the (non-)existence of such signed 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

Ars Math. Contemp.

自引率

0.00%

发文量