符号图矩阵树定理的再初等证明

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2023-08-29 DOI:10.1142/s1005386723000408

Shu Li, Jianfeng Wang

{"title":"符号图矩阵树定理的再初等证明","authors":"Shu Li, Jianfeng Wang","doi":"10.1142/s1005386723000408","DOIUrl":null,"url":null,"abstract":"A signed graph [Formula: see text] is a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], together with a function [Formula: see text] assigning a positive or negative sign to each edge. In this paper, we present a more elementary proof for the matrix-tree theorem of signed graphs, which is based on the relations between the incidence matrices and the Laplcians of signed graphs. As an application, we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Yet More Elementary Proof of Matrix-Tree Theorem for Signed Graphs\",\"authors\":\"Shu Li, Jianfeng Wang\",\"doi\":\"10.1142/s1005386723000408\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A signed graph [Formula: see text] is a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], together with a function [Formula: see text] assigning a positive or negative sign to each edge. In this paper, we present a more elementary proof for the matrix-tree theorem of signed graphs, which is based on the relations between the incidence matrices and the Laplcians of signed graphs. As an application, we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.\",\"PeriodicalId\":50958,\"journal\":{\"name\":\"Algebra Colloquium\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Colloquium\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1005386723000408\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Colloquium","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386723000408","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

带符号图[公式:见文]是一个具有顶点集[公式:见文]和边集[公式:见文]的图[公式:见文]，以及为每条边赋正号或负号的函数[公式:见文]。本文从关联矩阵与符号图的拉普拉斯定理的关系出发，给出了符号图的矩阵树定理的一个较为初等的证明。作为应用，我们也得到了monhad和Mallik关于无符号拉普拉斯图的矩阵树定理的结果。

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

Yet More Elementary Proof of Matrix-Tree Theorem for Signed Graphs

A signed graph [Formula: see text] is a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], together with a function [Formula: see text] assigning a positive or negative sign to each edge. In this paper, we present a more elementary proof for the matrix-tree theorem of signed graphs, which is based on the relations between the incidence matrices and the Laplcians of signed graphs. As an application, we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.

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

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.