TY - JOUR

T1 - Equitable 2-partitions of the Hamming graphs with the second eigenvalue

AU - Mogilnykh, Ivan

AU - Valyuzhenich, Alexandr

PY - 2020/11/1

Y1 - 2020/11/1

N2 - 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.

AB - 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.

KW - Completely regular code

KW - Eigenvalue technique

KW - Equitable partition

KW - Hamming graph

KW - MINIMUM SUPPORTS

UR - http://www.scopus.com/inward/record.url?scp=85087151789&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2020.112039

DO - 10.1016/j.disc.2020.112039

M3 - Article

AN - SCOPUS:85087151789

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 11

M1 - 112039

ER -