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

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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

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Bang, S., van Dam, E. R., & Koolen, J. H. (2007). Spectral Characterization of the Hamming Graphs. (CentER Discussion Paper; Vol. 2007-81). Operations research.

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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",

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

year = "2007",

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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 -