Volume 20, No 5, 2013, P. 3-12

UDC 519.1
Vorobev K. V.
On the embedding of eigenfunctions of the Johnson graph into eigenfunctions of the Hamming graph

Abstract:
We study a connection between eigenfunctions of the Johnson and Hamming graphs. An eigenfunction of a graph is an eigenvector with a given eigenvalue of its adjacency matrix, therewith an eigenfunction can be zero function. We find a criterion for embedding of the Johnson graph’s J(n,w) eigenfunction with a given eigenvalue in a certain Hamming graph’s eigenfunction with a given eigenvalue.
Bibliogr. 8.

Keywords: hypercube, Johnson and Hamming graphs, eigenvalue.

Vorobev Konstantin Vasil’evich ^1,2
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: konstantin.vorobev@gmail.com, vorobev@math.nsc.ru