Ostrander关于有向图拉普拉斯特征向量的三个猜想

Q3 Mathematics Art of Discrete and Applied Mathematics Pub Date : 2021-07-05 DOI:10.26493/2590-9770.1420.B57

Yaokun Wu, Da Zhao

{"title":"Ostrander关于有向图拉普拉斯特征向量的三个猜想","authors":"Yaokun Wu, Da Zhao","doi":"10.26493/2590-9770.1420.B57","DOIUrl":null,"url":null,"abstract":"Ostrander proposed three conjectures on the connections between topological properties of a weighted digraph and combinatorial properties of its Laplacian eigenvectors. We verify one of his conjectures, give counterexamples to the other two, and then seek for related valid connections and generalizations to Schrodinger operators on countable digraphs. We suggest the open question of deciding if the countability assumption can be dropped from our main results.","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Three conjectures of Ostrander on digraph Laplacian eigenvectors\",\"authors\":\"Yaokun Wu, Da Zhao\",\"doi\":\"10.26493/2590-9770.1420.B57\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Ostrander proposed three conjectures on the connections between topological properties of a weighted digraph and combinatorial properties of its Laplacian eigenvectors. We verify one of his conjectures, give counterexamples to the other two, and then seek for related valid connections and generalizations to Schrodinger operators on countable digraphs. We suggest the open question of deciding if the countability assumption can be dropped from our main results.\",\"PeriodicalId\":36246,\"journal\":{\"name\":\"Art of Discrete and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Art of Discrete and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/2590-9770.1420.B57\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Art of Discrete and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/2590-9770.1420.B57","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 1

摘要

Ostrander对加权有向图的拓扑性质与其拉普拉斯特征向量的组合性质之间的联系提出了三个猜想。我们验证了他的一个猜想，给出了另外两个猜想的反例，然后寻求可数有向图上薛定谔算子的相关有效联系和推广。我们建议讨论一个悬而未决的问题，即是否可以从我们的主要结果中去掉可数假设。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Three conjectures of Ostrander on digraph Laplacian eigenvectors

Ostrander proposed three conjectures on the connections between topological properties of a weighted digraph and combinatorial properties of its Laplacian eigenvectors. We verify one of his conjectures, give counterexamples to the other two, and then seek for related valid connections and generalizations to Schrodinger operators on countable digraphs. We suggest the open question of deciding if the countability assumption can be dropped from our main results.

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