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

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