Spectral Characterizations of Some Distance-Regular Graphs

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Abstract

When can one see from the spectrum of a graph whether it is distance-regular or not?We give some new results for when this is the case.As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2; 1), (3; 1) and (4; 1), the Biggs-Smith graph, the M22 graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages12
Volume793
Publication statusPublished - 2000

Publication series

NameFEW Research Memorandum
Volume793

Fingerprint

Distance-regular Graph
Graph in graph theory
Collinearity
Binary Code
Coset
Ternary

Keywords

  • graph theory
  • graphs

Cite this

van Dam, E. R., & Haemers, W. H. (2000). Spectral Characterizations of Some Distance-Regular Graphs. (FEW Research Memorandum; Vol. 793). Tilburg: Operations research.
van Dam, E.R. ; Haemers, W.H. / Spectral Characterizations of Some Distance-Regular Graphs. Tilburg : Operations research, 2000. 12 p. (FEW Research Memorandum).
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keywords = "graph theory, graphs",
author = "{van Dam}, E.R. and W.H. Haemers",
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van Dam, ER & Haemers, WH 2000, Spectral Characterizations of Some Distance-Regular Graphs. FEW Research Memorandum, vol. 793, vol. 793, Operations research, Tilburg.

Spectral Characterizations of Some Distance-Regular Graphs. / van Dam, E.R.; Haemers, W.H.

Tilburg : Operations research, 2000. 12 p. (FEW Research Memorandum; Vol. 793).

Research output: Book/ReportReportProfessional

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T1 - Spectral Characterizations of Some Distance-Regular Graphs

AU - van Dam, E.R.

AU - Haemers, W.H.

N1 - Pagination: 12

PY - 2000

Y1 - 2000

N2 - When can one see from the spectrum of a graph whether it is distance-regular or not?We give some new results for when this is the case.As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2; 1), (3; 1) and (4; 1), the Biggs-Smith graph, the M22 graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code.

AB - When can one see from the spectrum of a graph whether it is distance-regular or not?We give some new results for when this is the case.As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2; 1), (3; 1) and (4; 1), the Biggs-Smith graph, the M22 graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code.

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BT - Spectral Characterizations of Some Distance-Regular Graphs

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CY - Tilburg

ER -

van Dam ER, Haemers WH. Spectral Characterizations of Some Distance-Regular Graphs. Tilburg: Operations research, 2000. 12 p. (FEW Research Memorandum).