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

Aida Abiad Monge; Edwin R. van Dam; M.A. Fiol

doi:10.1016/j.jcta.2016.04.004

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

Aida Abiad Monge, Edwin R. van Dam, M.A. Fiol

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1-18
Journal	Journal of Combinatorial Theory Series A
Volume	143
DOIs	https://doi.org/10.1016/j.jcta.2016.04.004
Publication status	Published - Oct 2016

Keywords

distance-regular graph
Eigenvalues
girth
odd-girth
preintersection numbers

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10.1016/j.jcta.2016.04.004

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title = "Some spectral and quasi-spectral characterizations of distance-regular graphs",

abstract = "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.",

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author = "{Abiad Monge}, Aida and {van Dam}, {Edwin R.} and M.A. Fiol",

year = "2016",

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AU - Abiad Monge, Aida

AU - van Dam, Edwin R.

AU - Fiol, M.A.

PY - 2016/10

Y1 - 2016/10

N2 - 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.

AB - 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.

KW - distance-regular graph

KW - Eigenvalues

KW - girth

KW - odd-girth

KW - preintersection numbers

U2 - 10.1016/j.jcta.2016.04.004

DO - 10.1016/j.jcta.2016.04.004

M3 - Article

SN - 0097-3165

VL - 143

SP - 1

EP - 18

JO - Journal of Combinatorial Theory Series A

JF - Journal of Combinatorial Theory Series A

ER -

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

Abstract

Keywords

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