Authors: Stevanović, Dragan 
de Abreu, Nair
de Freitas, Maria
Del-Vecchio, Renata
Title: Walks and regular integral graphs
Journal: Linear Algebra and Its Applications
Volume: 423
Issue: 1
First page: 119
Last page: 135
Issue Date: 1-May-2007
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.11.026
Abstract: 
We establish a useful correspondence between the closed walks in regular graphs and the walks in infinite regular trees, which, after counting the walks of a given length between vertices at a given distance in an infinite regular tree, provides a lower bound on the number of closed walks in regular graphs. This lower bound is then applied to reduce the number of the feasible spectra of the 4-regular bipartite integral graphs by more than a half. Next, we give the details of the exhaustive computer search on all 4-regular bipartite graphs with up to 24 vertices, which yields a total of 47 integral graphs.
Keywords: Bipartite graphs | Graph eigenvalues | Integral graphs | Regular graphs
Publisher: Elsevier

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