Unimodular equivalence of graphs

DOI10.1016/0024-3795(92)90428-DzbMath0763.05071MaRDI QIDQ1194290

Russell Merris

Publication date: 27 September 1992

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Laplacian matrixchromatic polynomialSmith normal formdigraph flows

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (24)

A note on unimodular congruence of graphs ⋮ The sandpile group of a thick cycle graph ⋮ Small clique number graphs with three trivial critical ideals ⋮ Graphs with few trivial critical ideals ⋮ On the sandpile group of the square cycle \(C^{2}_{n}\) ⋮ The structure of sandpile groups of outerplanar graphs ⋮ On the critical group of the \(n\)-cube ⋮ Critical groups of simplicial complexes ⋮ Graphs whose critical groups have larger rank ⋮ Digraphs with at most one trivial critical ideal ⋮ Smith normal form of some distance matrices ⋮ The critical group of \(K_m \times P_n\) ⋮ Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields ⋮ Graphs with few trivial characteristic ideals ⋮ On the sandpile group of the cone of a graph ⋮ On the sandpile group of \(3\times n\) twisted bracelets ⋮ A note on unimodular congruence of the Laplacian matrix of a graph ⋮ Critical ideals of signed graphs with twin vertices ⋮ On the sandpile group of the graph \(K_{3}\times C_n\) ⋮ The critical group of \(K_{m} \times C_{n}\) ⋮ The sandpile group of a family of nearly complete graphs ⋮ On the minors of an incidence matrix and Smith normal form ⋮ Laplacian matrices of graphs: A survey ⋮ The critical group of a threshold graph

Cites Work

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• Parallel concepts in graph theory
• An edge version of the matrix-tree theorem and the wiener index
• Bicycles and Spanning Trees
• Matrix Generalizations of Some Theorems on Trees, Cycles and Cocycles in Graphs
• Coalescence, majorization, edge valuations and the laplacian spectra of graphs
• The laplacian matrix of a graph: unimodular congruence
• An introduction to chromatic polynomials

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