Walks and regular integral graphs |
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Authors: | Dragan Stevanovi? Nair MM de Abreu |
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Institution: | a University of Niš, Serbia and Montenegro b Federal University of Rio de Janeiro, Brazil c Federal University of Fluminense, Niteroi, Brazil |
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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. |
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Keywords: | 05C50 |
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