Algebraic Characterizations of Regularity Properties in Bipartite Graphs

Aida Abiad Monge, C. Dalfó, M.A. Fiol

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph ?? is distance-regular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distance-regularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the hoffman polynomial. Moreover, it is shown that the conditions for having distance-regularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.
Original languageEnglish
Pages (from-to)1223-1231
JournalEuropean Journal of Combinatorics
Volume34
Issue number8
DOIs
Publication statusPublished - Nov 2013

Cite this

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title = "Algebraic Characterizations of Regularity Properties in Bipartite Graphs",
abstract = "Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph ?? is distance-regular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distance-regularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the hoffman polynomial. Moreover, it is shown that the conditions for having distance-regularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.",
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Algebraic Characterizations of Regularity Properties in Bipartite Graphs. / Abiad Monge, Aida; Dalfó, C.; Fiol, M.A.

In: European Journal of Combinatorics, Vol. 34, No. 8, 11.2013, p. 1223-1231.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Dalfó, C.

AU - Fiol, M.A.

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AB - Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph ?? is distance-regular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distance-regularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the hoffman polynomial. Moreover, it is shown that the conditions for having distance-regularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.

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