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

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

Research output: Contribution to journalArticleScientificpeer-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
JournalJournal of Combinatorial Theory, Series A, Structures designs and application combinatorics
Volume143
DOIs
Publication statusPublished - Oct 2016

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Distance-regular Graph
Girth
Graph in graph theory
Intersection number
Adjacency Matrix
Odd
Regularity
Generalise

Keywords

  • distance-regular graph
  • Eigenvalues
  • girth
  • odd-girth
  • preintersection numbers

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.",
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Some spectral and quasi-spectral characterizations of distance-regular graphs. / Abiad Monge, Aida; van Dam, Edwin; Fiol, M.A.

In: Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics, Vol. 143, 10.2016, p. 1-18.

Research output: Contribution to journalArticleScientificpeer-review

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AU - van Dam, Edwin

AU - Fiol, M.A.

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KW - distance-regular graph

KW - Eigenvalues

KW - girth

KW - odd-girth

KW - preintersection numbers

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DO - 10.1016/j.jcta.2016.04.004

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