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

260 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

Fingerprint

Distance-regular Graph
Excess
Regularity
Theorem
Eigenspace
Regularity Properties
Concepts

Keywords

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

Cite this

Dalfo, C. ; van Dam, E.R. ; Fiol, M.A. ; Garriga, E. / Dual concepts of almost distance-regularity and the spectral excess theorem. In: Discrete Mathematics. 2012 ; Vol. 312, No. 17. pp. 2730-2734.
@article{2feeed57690544cd90beed12a67bf5c8,
title = "Dual concepts of almost distance-regularity and the spectral excess theorem",
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.",
keywords = "distance-regular graph, distance matrices, Eigenvalues, idempotents, local spectrum, predistance polynomials",
author = "C. Dalfo and {van Dam}, E.R. and M.A. Fiol and E. Garriga",
year = "2012",
month = "9",
doi = "10.1016/j.disc.2012.03.003",
language = "English",
volume = "312",
pages = "2730--2734",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "17",

}

Dual concepts of almost distance-regularity and the spectral excess theorem. / Dalfo, C.; van Dam, E.R.; Fiol, M.A.; Garriga, E.

In: Discrete Mathematics, Vol. 312, No. 17, 09.2012, p. 2730-2734.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Dual concepts of almost distance-regularity and the spectral excess theorem

AU - Dalfo, C.

AU - van Dam, E.R.

AU - Fiol, M.A.

AU - Garriga, E.

PY - 2012/9

Y1 - 2012/9

N2 - 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.

AB - 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.

KW - distance-regular graph

KW - distance matrices

KW - Eigenvalues

KW - idempotents

KW - local spectrum

KW - predistance polynomials

U2 - 10.1016/j.disc.2012.03.003

DO - 10.1016/j.disc.2012.03.003

M3 - Article

VL - 312

SP - 2730

EP - 2734

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 17

ER -