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Wiener index and graphs, almost half of whose vertices satisfy Šoltés property
Margarita Akhmejanova, Konstantin Olmezov, Aleksei Volostnov +3
The Wiener index of a connected graph is a sum of distances between all pairs of vertices of . In 1991, Šoltés formulated the problem of finding all graphs such t…
Equitable 2-partitions of Johnson graphs with the second eigenvalue
Konstantin Vorob'ev
We study equitable 2-partitions of the Johnson graphs J(n,w) with a quotient matrix containing the eigenvalue lambda_2(w,n) = (w-2)(n-w-2)-2 in its spectrum. For any w>=4 and n>=2w…
Perfect 2-colorings of Hamming graphs
Evgeny A. Bespalov, Denis S. Krotov, Aleksandr A. Matiushev +2
We consider the problem of existence of perfect -colorings (equitable -partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs a…
On reconstruction of eigenfunctions of Johnson graphs
Konstantin Vorob'ev
In the present work we consider the problem of a reconstruction of eigenfunctions of the Johnson graph . We give necessary and sufficient numerical conditions for a unique…
Minimum supports of eigenfunctions of Johnson graphs
Konstantin Vorob'ev, Ivan Mogilnykh, Alexandr Valyuzhenich
We study the weights of eigenvectors of the Johnson graphs . For any and sufficiently large we show that an eigenvector of …