对称群上交换图的完备码  

Perfect Codes in Commuting Graphs of Symmetric Groups

作　　者：马儇龙 钟国 王恺顺[5,6] Xuan Long MA;Guo ZHONG;Kai Shun WANG(School of Science,Xi'an Shiyou University,Xi'an 710065,P.R.China;School of Computer Science,Xi'an Shiyou University,Xi'an 710065,P.R.China;School of Information Science and Technology,Guangdong University of Foreign Studies,Guangzhou 510006,P.R.China;Guangzhou Key Laboratory of Multilingual Intelligent Processing,Guangzhou 510006,P.R.China;School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China;Laboratory for Mathematics and Complea Systems,Beijing 100875,P.R.China)

机构地区：[1]西安石油大学理学院,西安710065 [2]西安石油大学计算机学院,西安710065 [3]广东外语外贸大学信息科学与技术学院,广州510006 [4]广州市非通用语种智能处理重点实验室,广州510006 [5]北京师范大学数学科学学院,北京100875 [6]数学与复杂系统教育部重点实验室,北京100875

出　　处：《数学学报（中文版）》2023年第3期475-484,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家重点研发计划(2020YFA0712900);国家自然科学基金(11801441,12071039,12131011);陕西省自然科学基金(2020JQ-761);陕西省高校科协青年人才托举计划(20190507)。

摘　　要：设G是一个有限群,G上的交换图以G中非中心元素构成的集合为顶点集,其中两个不同的顶点x,y相邻当且仅当xy=yx.图的完备码问题是指:判断图是否具有完备码;如果图具有完备码,则如何找到该图的完备码.本文解决了对称群和交错群上交换图的完备码问题.Let G be a finite group.The commuting graph of G is a graph whose vertex set is the set of all non-central elements,and two distinct vertices and y are adjacent if and only if xy=yx.The graph perfect code problem is as follows:determine whether a graph admits perfect codes;if a graph admits a perfect code,then how do we find the perfect codes.In this paper,we solve the perfect code problem of the commuting graphs of symmetric groups and alternating groups.

关 键 词：交换图 完备码 对称群 交错群 

分 类 号：O152.1[理学—数学]