On the embedding of eigenfunctions of the Johnson graph into eigenfunctions of the Hamming graph
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 5, pp. 3-12.

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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.
Mots-clés : hypercube
Keywords: Johnson and Hamming graphs, eigenvalue.
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K. V. Vorobev. On the embedding of eigenfunctions of the Johnson graph into eigenfunctions of the Hamming graph. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 5, pp. 3-12. http://geodesic.mathdoc.fr/item/DA_2013_20_5_a0/

[1] Avgustinovich S. V., Vasileva A. Yu., “Teoremy vosstanovleniya dlya tsentrirovannykh funktsii i sovershennykh kodov”, Sib. mat. zhurn., 49:3 (2008), 483–489 | MR | Zbl

[2] Avgustinovich S. V., Mogilnykh I. Yu., “Sovershennye raskraski grafov Dzhonsona $J(8,3)$ i $J(8,4)$ v dva tsveta”, Diskret. analiz i issled. operatsii, 17:2 (2010), 3–19 | MR | Zbl

[3] Vasileva A. Yu., “O rekonstruktivnykh mnozhestvakh vershin v bulevom kube”, Diskret. analiz i issled. operatsii, 19:1 (2012), 3–16 | MR

[4] Delsart F., Algebraicheskii podkhod k skhemam otnoshenii teorii kodirovaniya, Mir, M., 1976, 136 pp. | MR

[5] Mak-Vilyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1994, 744 pp.

[6] Avgustinovich S. V., Mogil'nykh I. Yu., “Induced perfect colorings”, Sib. elektron. mat. izv., 8 (2011), 310–316 | MR

[7] Martin W. J., “Completely regular designs of strength one”, J. Algebr. Comb., 3 (1994), 177–185 | DOI | MR | Zbl

[8] Martin W. J., “Completely regular designs”, J. Comb. Des., 4 (1998), 261–273 | 3.0.CO;2-D class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl