В рамките на онлайн семинара
Problems and Methods Related to Coding Theory
организиран от:
Института по математика и информатика на Българската академия на науките,
Новосибирския държавен университет, Новосибирск, Русия,
Института по математика “С. Л. Соболев”, Сибирски клон на Руската академия на науките, Новосибирск, Русия,
на 2 февруари 2021 г. от 13:00 ч. (18:00 ч. в Новосибирск, 14:00 ч. в Москва)
проф. Сергей Августинович, Институт по математика “С. Л. Соболев”, Новосибирск, Русия,
ще изнесе доклад на тема:
Совершенные раскраски циркулянтных графов
(Perfect colorings of circulant graphs).
Резюме: A Cayley graph of the infinite cyclic group having generators d1, d2, d3, …, dn is called circulant. It is denoted by С∞(d1, d2, d3, …, dn). A coloring of the vertex set of a graph is called perfect if for any colors i and j and any vertex x of color i, the number of its neighbors of color j depends only on i and j. It is well known that any perfect coloring of an infinite circulant graph is periodic.
There is a natural homomorphism from the n-dimensional lattice into an arbitrary circulant graph with n distances. In particular, this рmeans that every perfect coloring of a circulant graph with n distances induces a perfect coloring of an n-dimensional rectangular lattice with the same parameters. In the talk some constructions of colorings and open questions will be considered.
Time: Feb 2, 2021, 13:00 Sofia (18:00 Novosibirsk, 14:00 Moscow)
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