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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