Some spectral and quasi-spectral characterizations of distance-regular graphs

In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quas...

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Veröffentlicht in:Journal of combinatorial theory. Series A Jg. 143; S. 1 - 18
Hauptverfasser: Abiad, A., van Dam, E.R., Fiol, M.A.
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.10.2016
Schlagworte:
05 Combinatorics
05C Graph theory
05E Algebraic combinatorics
Classificació AMS
Combinatorial analysis
Combinatòria
Distance-regular graph
Eigenvalues
Girth
Grafs, Teoria de
Graph theory
Matemàtica discreta
Matemàtiques i estadística
Odd-girth
Preintersection numbers
Teoria de grafs
Àrees temàtiques de la UPC
Distance-regular graph
Eigenvalues
Girth
Preintersection numbers
Odd-girth
ISSN:0097-3165, 1096-0899
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Zusammenfassung:In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2016.04.004