Spectral characterizations of the Hamming graph

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

Spectral characterizations of the Hamming graph

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
Pages (from-to)	2678-2686
Journal	Linear Algebra and its Applications
Volume	429
Issue number	11-12
Publication status	Published - 2008

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title = "Spectral characterizations of the Hamming graph",

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.",

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

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AU - Bang, S.

AU - van Dam, E.R.

AU - Koolen, J.H.

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Y1 - 2008

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.

M3 - Article

SN - 0024-3795

VL - 429

SP - 2678

EP - 2686

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - 11-12

ER -

Spectral characterizations of the Hamming graph

Abstract

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