A note on unimodular congruence of graphs
type: Item
instance of: scholarly article
title: A note on unimodular congruence of graphs
zbMATH Open document ID: 0807.05054
DOI: 10.1016/0024-3795(94)90104-X
author: Russell Merris
published in: Linear Algebra and its Applications
publication date: 1994-08-15T00:00:00Z
review text: Let \(Q= Q(G)\) be an oriented vertex-edge incidence matrix of the graph \(G\). Then \(L(G)= QQ^ t\) is the Laplacian matrix of \(G\) and \(K(G)= Q^ t Q\) is an edge version of the Laplacian. In this note it is shown that for connected graphs \(G\), \(H\), associated matrices \(K(G)\) and \(K(H)\), respectively, are unimodularly congruent if and only if \(G\) and \(H\) have the same number of vertices and the same number of edges. The related problem of unimodular congruence of Laplacian matrices has been recently solved by \textit{W. Watkins} [Unimodular congruence of the Laplacian matrix of a graph, Linear Algebra Appl. 201, 43-49 (1994; next review)].
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 614170
zbMATH Keywords: Laplacian matrix
zbMATH Keywords: unimodular congruence
reviewed by: Bojan Mohar
MaRDI profile type: Publication
cites work: Q4770409
cites work: Line graphs, root systems, and elliptic geometry
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cites work: Unimodular equivalence of graphs
cites work: Laplacian matrices of graphs: A survey
cites work: Q5668937
cites work: Principal subpermanents of the Laplacian matrix
cites work: Unimodular congruence of the Laplacian matrix of a graph
description: scientific article; zbMATH DE number 614170