A characterization of bipartite distance-regular graphs

Guang Siang Lee*, Chih-wen Weng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

It is well-known that the halved graphs of a bipartite distance-regular graph are distance-regular. Examples are given to show that the converse does not hold. Thus, a natural question is to find out when the converse is true. In this paper we give a quasi-spectral characterization of a connected bipartite weighted 2-punctually distance-regular graph whose halved graphs are distance-regular. In the case the spectral diameter is even we show that the graph characterized above is distance-regular.

Original languageEnglish
Pages (from-to)91-103
Number of pages13
JournalLinear Algebra and Its Applications
Volume446
DOIs
StatePublished - 1 Apr 2014

Keywords

  • Distance matrices
  • Distance-regular graph
  • Predistance polynomials
  • Spectral diameter
  • Spectral excess theorem

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