As part of the online seminar
Problems and Methods Related to Coding Theory
organized by:
the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
the Novosibirsk State University, Novosibirsk, Russia
the Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
on February 2, 2021, 1:00 pm Sofia (6:00 pm Novosibirsk, 2:00 pm Moscow)
Prof. Sergey Avgustinovich, Sobolev Institute of Mathematics, Novosibirsk, Russia
will deliver a talk on:
Совершенные раскраски циркулянтных графов
(Perfect colorings of circulant graphs).
Abstract: 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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