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math.CO2025
On strong nodal domains for eigenfunctions of Hamming graphs
Alexandr Valyuzhenich, Konstantin Vorob'ev
The Laplacian matrix of the -dimensional hypercube has distinct eigenvalues , where . In 2004, Bıyıkoğlu, Hordijk, Leydold, Pisanski and Stadler initiat…
math.CO2024
Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs
Ivan Mogilnykh, Anna Taranenko, Konstantin Vorob'ev
We obtain a classification of the completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs H(3,q) up to q and intersection array. Due to work…
math.CO2023
Some results on the Wiener index related to the Šoltés problem of graphs
Andrey A. Dobrynin, Konstantin V. Vorob'ev
The Wiener index, , of a connected graph is the sum of distances between its vertices. In 2021, Akhmejanova et al. posed the problem of finding graphs with large $R_m…