Spectral Characterization of the Hamming Graphs

S. Bang; E.R. van Dam; J.H. Koolen

Spectral Characterization of the Hamming Graphs

S. Bang, E.R. van Dam, J.H. Koolen

Research output: Working paper › Discussion paper › Other research output

247 Downloads (Pure)

Abstract

We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q ¸ 36. Moreover, we show that for given integer D ¸ 2, any graph cospectral with the Hamming graph H(D; q) is locally the disjoint union of D copies of the complete graph of size q ¡ 1, for q large enough.

Original language	English
Place of Publication	Tilburg
Publisher	Operations research
Number of pages	14
Volume	2007-81
Publication status	Published - 2007

Publication series

Name	CentER Discussion Paper
Volume	2007-81

Keywords

Hamming graphs
distance-regular graphs
eigenvalues of graphs

Access to Document

Dp2007-81

Fingerprint Dive into the research topics of 'Spectral Characterization of the Hamming Graphs'. Together they form a unique fingerprint.

Cite this

@techreport{6c76624a373043b0b2099f6dddf7b766,

title = "Spectral Characterization of the Hamming Graphs",

abstract = "We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q ¸ 36. Moreover, we show that for given integer D ¸ 2, any graph cospectral with the Hamming graph H(D; q) is locally the disjoint union of D copies of the complete graph of size q ¡ 1, for q large enough.",

keywords = "Hamming graphs, distance-regular graphs, eigenvalues of graphs",

author = "S. Bang and {van Dam}, E.R. and J.H. Koolen",

note = "Subsequently published in Linear Algebra and its Applications, 2008 Pagination: 14",

year = "2007",

language = "English",

volume = "2007-81",

series = "CentER Discussion Paper",

publisher = "Operations research",

type = "WorkingPaper",

institution = "Operations research",

}

TY - UNPB

T1 - Spectral Characterization of the Hamming Graphs

AU - Bang, S.

AU - van Dam, E.R.

AU - Koolen, J.H.

N1 - Subsequently published in Linear Algebra and its Applications, 2008 Pagination: 14

PY - 2007

Y1 - 2007

N2 - We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q ¸ 36. Moreover, we show that for given integer D ¸ 2, any graph cospectral with the Hamming graph H(D; q) is locally the disjoint union of D copies of the complete graph of size q ¡ 1, for q large enough.

AB - We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q ¸ 36. Moreover, we show that for given integer D ¸ 2, any graph cospectral with the Hamming graph H(D; q) is locally the disjoint union of D copies of the complete graph of size q ¡ 1, for q large enough.

KW - Hamming graphs

KW - distance-regular graphs

KW - eigenvalues of graphs

M3 - Discussion paper

VL - 2007-81

T3 - CentER Discussion Paper

BT - Spectral Characterization of the Hamming Graphs

PB - Operations research

CY - Tilburg

ER -