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

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

Research output: Contribution to journalArticleAcademicpeer-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 languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal of Combinatorial Theory Series A
Volume143
DOIs
Publication statusPublished - 2016

Keywords

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

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",
note = "No data used.",
year = "2016",
doi = "10.1016/j.jcta.2016.04.004",
language = "English",
volume = "143",
pages = "1--18",
journal = "Journal of Combinatorial Theory Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",

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Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs. / Abiad Monge, Aida; van Dam, E.R. ; Fiol, M.A.

In: Journal of Combinatorial Theory Series A, Vol. 143, 2016, p. 1-18.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs

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AU - Fiol, M.A.

N1 - No data used.

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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

VL - 143

SP - 1

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JO - Journal of Combinatorial Theory Series A

JF - Journal of Combinatorial Theory Series A

SN - 0097-3165

ER -