Dual concepts of almost distance-regularity and the spectral excess theorem

C. Dalfo, E.R. van Dam, M.A. Fiol, E. Garriga

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
298 Downloads (Pure)

Abstract

Generally speaking, ‘almost distance-regular’ graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize m-partially distance-regular graphs and j-punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it.
Original languageEnglish
Pages (from-to)2730-2734
JournalDiscrete Mathematics
Volume312
Issue number17
DOIs
Publication statusPublished - Sep 2012

Keywords

  • distance-regular graph
  • distance matrices
  • Eigenvalues
  • idempotents
  • local spectrum
  • predistance polynomials

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