Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs

Aida Abiad Monge; E.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^*, E.R. van Dam, M.A. Fiol

^*Corresponding author for this work

QE Operations research

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

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
Number of pages	18
Journal	Journal of Combinatorial Theory Series A
Volume	143
DOIs	https://doi.org/10.1016/j.jcta.2016.04.004
Publication status	Published - 2016

Keywords

Distance-regular graph
Eigenvalues
Girth
Odd-girth
Preintersection numbers
EXCESS THEOREM
POLYNOMIALS

Access to Document

10.1016/j.jcta.2016.04.004

Cite this

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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. ",

keywords = "Distance-regular graph, Eigenvalues, Girth, Odd-girth, Preintersection numbers, EXCESS THEOREM, POLYNOMIALS",

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

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language = "English",

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pages = "1--18",

journal = "Journal of Combinatorial Theory Series A",

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AU - van Dam, E.R.

AU - Fiol, M.A.

N1 - No data used.

PY - 2016

Y1 - 2016

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

KW - EXCESS THEOREM

KW - POLYNOMIALS

U2 - 10.1016/j.jcta.2016.04.004

DO - 10.1016/j.jcta.2016.04.004

M3 - Article

SN - 0097-3165

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SP - 1

EP - 18

JO - Journal of Combinatorial Theory Series A

JF - Journal of Combinatorial Theory Series A

ER -