Equitable 2-partitions of the Hamming graphs with the second eigenvalue

Ivan Mogilnykh, Alexandr Valyuzhenich

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1 Citation (Scopus)

Abstract

The eigenvalues of the Hamming graph H(n,q) are known to be λi(n,q)=(q−1)n−qi, 0≤i≤n. The characterization of equitable 2-partitions of the Hamming graphs H(n,q) with eigenvalue λ1(n,q) was obtained by Meyerowitz (2003). We study the equitable 2-partitions of H(n,q) with eigenvalue λ2(n,q). We show that these partitions are reduced to equitable 2-partitions of H(3,q) with eigenvalue λ2(3,q) with the exception of two constructions.

Original languageEnglish
Article number112039
Number of pages9
JournalDiscrete Mathematics
Volume343
Issue number11
DOIs
Publication statusPublished - 1 Nov 2020

Keywords

  • Completely regular code
  • Eigenvalue technique
  • Equitable partition
  • Hamming graph
  • MINIMUM SUPPORTS

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