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 languageEnglish
Pages (from-to)2678-2686
JournalLinear Algebra and its Applications
Volume429
Issue number11-12
Publication statusPublished - 2008

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Hamming Graph
Cospectral Graphs
Complete Graph
Disjoint
Union
Integer

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Bang, S. ; van Dam, E.R. ; Koolen, J.H. / Spectral characterizations of the Hamming graph. In: Linear Algebra and its Applications. 2008 ; Vol. 429, No. 11-12. pp. 2678-2686.
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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.",
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note = "Appeared earlier as CentER Discussion Paper 2007-81",
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volume = "429",
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Bang, S, van Dam, ER & Koolen, JH 2008, 'Spectral characterizations of the Hamming graph', Linear Algebra and its Applications, vol. 429, no. 11-12, pp. 2678-2686.

Spectral characterizations of the Hamming graph. / Bang, S.; van Dam, E.R.; Koolen, J.H.

In: Linear Algebra and its Applications, Vol. 429, No. 11-12, 2008, p. 2678-2686.

Research output: Contribution to journalArticleScientificpeer-review

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T1 - Spectral characterizations of the Hamming graph

AU - Bang, S.

AU - van Dam, E.R.

AU - Koolen, J.H.

N1 - Appeared earlier as CentER Discussion Paper 2007-81

PY - 2008

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

VL - 429

SP - 2678

EP - 2686

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

IS - 11-12

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