A infinity-graph is a graph consisting of two cycles with just a vertex in common. We first look for some invariants for cospectral graphs, then we introduce a new method to determine the degree sequence of cospectral mates of a graph. In this paper, we prove that all infinity-graphs without triangles are determined by their Laplacian spectra and that all infinity-graphs, with one exception, are determined by their signless Laplacian spectra. For the exception we determine all graphs that are cospectral (w.r.t. signless Laplacian spectrum) to it. (C) 2010 Elsevier B.V. All rights reserved.
On the spectral characterizations of infinity-graphs
BELARDO, FRANCESCO;LI MARZI, Enzo
2010-01-01
Abstract
A infinity-graph is a graph consisting of two cycles with just a vertex in common. We first look for some invariants for cospectral graphs, then we introduce a new method to determine the degree sequence of cospectral mates of a graph. In this paper, we prove that all infinity-graphs without triangles are determined by their Laplacian spectra and that all infinity-graphs, with one exception, are determined by their signless Laplacian spectra. For the exception we determine all graphs that are cospectral (w.r.t. signless Laplacian spectrum) to it. (C) 2010 Elsevier B.V. All rights reserved.File in questo prodotto:
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