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A finite group attached to the laplacian of a graph. (English) Zbl 0755.05079
The laplacian of a graph is the difference of the diagonal matrix giving the degrees of vertices and the adjacency matrix. The group in question is in effect the torsion part of the cokernel of the mapping on \(Z^ n\) induced by the laplacian. The author classifies graphs where its minimum number of cyclic generators is \(n-1\) or \(n-2\) and describes how the group changes when each edge of a graph is divided into \(k\) edges.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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References:
[1] Biggs, N., Algebraic graph theory, () · Zbl 0284.05101
[2] Lorenzini, D., Arithmetical graphs, Math. ann., 285, 481-501, (1989) · Zbl 0662.14008
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