Digraphs with at most one trivial critical ideal

被引：6

作者：

Alfaro, Carlos A. ^{[1
]}

Valencia, Carlos E. ^{[2
]}

Vazquez-Avila, Adrian ^{[3
]}

机构：

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

[2] IPN, Dept Matemat, Ctr Invest & Estudios Avanzados, Mexico City, DF, Mexico

[3] Univ Aeronaut Queretaro, Subdirecc Ingn & Posgrado, Queretaro, Mexico

来源：

LINEAR & MULTILINEAR ALGEBRA | 2018年 / 66卷 / 10期

关键词：

Critical ideal; critical group; Smith group; Laplacian matrix; forbidden induced subgraph; Smith normal form; SMITH NORMAL-FORM; SANDPILE GROUP; GRAPHS;

D O I：

10.1080/03081087.2017.1383349

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterization of the digraphs with at most one trivial critical ideal. Which implies the characterizations of the digraphs whose critical group has one invariant factor equal to one, and the digraphs whose Smith group has one invariant factor equal to one.

引用

页码：2036 / 2048

页数：13

共 24 条

[1]

Alfaro C.A., 2015, ELECT NOTES DISCRETE, V50, P391

[2]

Alfaro CA, 2013, ARXIV 1311 5927

[3] Critical ideals of signed graphs with twin vertices [J].