数学杂志2025，Vol.45Issue(5)：429-434,6.
若干有限非交换群上交换图的完备码
PERFECT CODES IN COMMUTING GRAPHS ON SEVERAL FINITE NON-ABELIAN GROUPS
摘要
Abstract
Let G be a finite non-abelian group.The commuting graph Γ(G)on group G has vertex set G\Z(G),and two vertices a and b are adjacent if and only if ab=ba,where Z(G)denotes the center of the group G.A subset C of the vertex set V(Γ)in graph Γ is a perfect code if C is an independent set of V(Γ)and each vertex in V(Γ)\C is adjacent to exactly one vertex in C.The problem of determining the existence of perfect codes and constructing such codes on commuting graphs is an important research topic.This paper presents some perfect codes of commuting graphs on some non-abelian groups.关键词
非交换群/交换图/完备码/半二面体群Key words
non-abelian group/commuting graph/perfect code/semidihedral group分类
数理科学引用本文复制引用
霍丽君,易光莉,李明丹..若干有限非交换群上交换图的完备码[J].数学杂志,2025,45(5):429-434,6.基金项目
重庆市自然科学基金项目(CSTB2022NSCQ-MSX0831,cstc2021jcyj-msxmX0575) （CSTB2022NSCQ-MSX0831,cstc2021jcyj-msxmX0575）
重庆理工大学研究生教育高质量发展行动计划资助成果(gzljg2022319,gzlcx20253353,gzlcx20253360) （gzljg2022319,gzlcx20253353,gzlcx20253360）
重庆理工大学教育教学改革项目(2023YB115,2023YB132) （2023YB115,2023YB132）
重庆理工大学高等教育研究项目(2024YB08). （2024YB08）
