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 languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages14
Volume2007-81
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-81

Keywords

  • Hamming graphs
  • distance-regular graphs
  • eigenvalues of graphs

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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.