Perfect colorings of the infinite circulant graph with distances 1 and 2

被引：0

作者：

Lisitsyna M.A. ^{[1
]}

Parshina O.G. ^{[2
,3
]}

机构：

[1] Marshal Budyonny Military Academy of Telecommunications, Tikhoretskii pr. 3, St. Petersburg

[2] Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk

[3] Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 Boulevard du 11 novembre 1918, Villeurbanne Cedex

来源：

Journal of Applied and Industrial Mathematics | 2017年 / 11卷 / 03期

关键词：

circulant graph; equitable partition; perfect coloring;

D O I：

10.1134/S1990478917030097

中图分类号：

学科分类号：

摘要：

A coloring of the vertex set in a graph is called perfect if all its identically colored vertices have identical multisets of colors of their neighbors. Refer as the infinite circulant graph with continuous set of n distances to the Cayley graph of the group ℤ with generator set {1, 2,.., n}. We obtain a description of all perfect colorings with an arbitrary number of colors of this graph with distances 1 and 2. In 2015, there was made a conjecture characterizing perfect colorings for the infinite circulant graphs with a continuous set of n distances. The obtained result confirms the conjecture for n = 2. The problem is still open in the case of n > 2. © 2017, Pleiades Publishing, Ltd.

引用

页码：381 / 388

页数：7

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