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Quasi-amply-regularity and Generalized Hamming Graphs

Authors
Journal
Electronic Notes in Discrete Mathematics
1571-0653
Publisher
Elsevier
Publication Date
Volume
22
Identifiers
DOI: 10.1016/j.endm.2005.06.020
Keywords
  • Amply-Regularity
  • Quasi-Amply-Regularity
  • Generalized Hamming Graph

Abstract

Abstract Let G λ be the class of the amply-regular graphs with parameters ( n , k , λ , 2 ) and G λ 1 , λ 2 be the one of the quasi-amply-regular graphs with parameters ( n , k , λ 1 , λ 2 , 2 ) . We first give some particular properties of G 1 with new proofs and a new characterization of the Hamming graphs H( d, 3). Then under some conditions, we provides a characterization of the generalized Hamming graphs H ( d 1 , λ 1 + 2 ; d 2 , λ 2 + 2 ) obtained by a cartesian product of H ( d 1 , λ 1 + 2 ) and H ( d 2 , λ 2 + 2 ) as a quasi-amply-regular graphs with parameters ( n , k , λ 1 , λ 2 , 2 ) of maximum order for a given degree.

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