Unimodular congruence of the Laplacian matrix of a graph
Copyright policy )Unimodular congruence of the Laplacian matrix of a graph
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 Laplacian matrices \(L(G)\) and \(L(H)\) of graphs \(G\) and \(H\), respectively, are unimodularly congruent if and only if \(G\) and \(H\) are cycle isomorphic. The related problem of unimodular congruence of Laplacian matrices has been recently solved by \textit{R. Merris} [A note on unimodular congruence of graphs, Linear Algebra Appl. 201, 57-60 (1994; preceding review)].
- California State University System United States
- California State University, Northridge United States
Numerical Analysis, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), unimodular congruence, Discrete Mathematics and Combinatorics, Geometry and Topology, Laplacian matrix
Numerical Analysis, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), unimodular congruence, Discrete Mathematics and Combinatorics, Geometry and Topology, Laplacian matrix
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