Distance ideals of graphs

被引：7

作者：

Alfaro, Carlos A. ^{[1
]}

Taylor, Libby ^{[2
]}

机构：

[1] Banco Mexico, Mexico City, DF, Mexico

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 584卷

关键词：

Smith normal form; Distance ideals; Distance matrix; Distance spectra; Graph; SMITH NORMAL-FORM; EQUIVALENCE; RANK;

D O I：

10.1016/j.laa.2019.09.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the concept of distance ideals of graphs, which can be regarded as a generalization of the Smith normal form and the spectra of the distance matrix and the Laplacian distance matrix of a graph. We also obtain a classification of the graphs with at most one trivial distance ideal. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：127 / 144

页数：18

共 27 条

[1] Alfaro C.A., 2018, ARXIV180707992
[2] Critical ideals, minimum rank and zero forcing number
Alfaro, Carlos A.
Lin, Jephian C-H
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 358 : 305 - 313
[3] Graphs with real algebraic co-rank at most two
Alfaro, Carlos A.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 556 : 100 - 107
[4] Digraphs with at most one trivial critical ideal
Alfaro, Carlos A.
Valencia, Carlos E.
Vazquez-Avila, Adrian
[J]. LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (10) : 2036 - 2048
[5] Small clique number graphs with three trivial critical ideals
Alfaro, Carlos A.
Valencia, Carlos E.
[J]. SPECIAL MATRICES, 2018, 6 (01): : 122 - 154
[6] Critical ideals of signed graphs with twin vertices
Alfaro, Carlos A.
Corrales, Hugo
Valencia, Carlos E.
[J]. ADVANCES IN APPLIED MATHEMATICS, 2017, 86 : 99 - 131
[7] Graphs with two trivial critical ideals
Alfaro, Carlos A.
Valencia, Carlos E.
[J]. DISCRETE APPLIED MATHEMATICS, 2014, 167 : 33 - 44
[8] On the sandpile group of the cone of a graph
Alfaro, Carlos A.
Valencia, Carlos E.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (05) : 1154 - 1176
[9] Distance spectra of graphs: A survey
Aouchiche, Mustapha
Hansen, Pierre
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 458 : 301 - 386
[10] Smith normal form of some distance matrices
Bapat, Ravindra B.
Karimi, Masoud
[J]. LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (06) : 1117 - 1130

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