Characterization of subgroup perfect codes in Cayley graphs

Chen，Jiyong1; Wang，Yanpeng2,3; Xia，Binzhou4

2020-05-01

10.1016/j.disc.2020.111813

DISCRETE MATHEMATICS   影响因子和分区

0012-365X

1872-681X

A subset C of the vertex set of a graph Γ is called a perfect code in Γ if every vertex of Γ is at distance no more than 1 to exactly one vertex of C. A subset C of a group G is called a perfect code of G if C is a perfect code in some Cayley graph of G. In this paper we give sufficient and necessary conditions for a subgroup H of a finite group G to be a perfect code of G. Based on this, we determine the finite groups that have no nontrivial subgroup as a perfect code, which answers a question by Ma, Walls, Wang and Zhou.

Cayley graph Cyclic group Generalized quaternion group Perfect code

SCI

英语

第一

China Scholarship Council[201806010040]

Mathematics

Mathematics

WOS:000528201500014

ELSEVIER

MATHEMATICS

2-s2.0-85077747065

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Guangdong,Shenzhen,518055,China
2.School of Mathematical Sciences,Peking University,Beijing,100871,China
3.Rongcheng Campus,Harbin University of Science and Technology,Heilongjiang,Harbin,150080,China
4.School of Mathematics and Statistics,The University of Melbourne,VIC,Parkville,3010,Australia

Chen，Jiyong,Wang，Yanpeng,Xia，Binzhou. Characterization of subgroup perfect codes in Cayley graphs[J]. DISCRETE MATHEMATICS,2020,343(5).

Chen，Jiyong,Wang，Yanpeng,&Xia，Binzhou.(2020).Characterization of subgroup perfect codes in Cayley graphs.DISCRETE MATHEMATICS,343(5).

Chen，Jiyong,et al."Characterization of subgroup perfect codes in Cayley graphs".DISCRETE MATHEMATICS 343.5(2020).