若干特殊二面体群的正规子群包含图的谱  

Spectra of normal subgroup inclusion graphs ofseveral special dihedral groups

作　　者：霍丽君 冉莎 HUO Lijun;RAN Sha(College of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《重庆理工大学学报（自然科学）》2023年第8期334-341,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：重庆市自然科学基金项目(CSTB2022NSCQ-MSX0831,cstc2021jcyj-msxmX0575);重庆理工大学研究生教育高质量发展行动计划项目(gzljg2022319,gzlcx20223306);重庆理工大学自科基金培育项目(2022PYZ023)。

摘　　要：利用有限群的非平凡的正规子群为顶点集构造了一类简单无向图,称为有限群的正规子群包含图,该图的2个顶点H、K相邻当且仅当H K或K H。对若干特殊二面体群D 2n的正规子群包含图In(D 2n)的相关谱参数进行了研究,得到了该图的邻接谱、拉普拉斯谱以及拟拉普拉斯谱等。In this paper,a class of simple undirected graphs called normal subgroup inclusion graphs are constructed by using the nontrivial normal subgroups of finite groups as its vertex set,and the two vertices K and H of the graph are adjacent if and only if H K or K H.In this paper,the spectral of normal subgroup inclusion graphs In(D 2n)of some special dihedral groups D 2n are studied,and the adjacency spectra,Laplacian spectra and quasi-Laplacian spectra of these graphs are obtained.

关 键 词：二面体群 正规子群包含图 图的谱 邻接谱 (拟)拉普拉斯谱 

分 类 号：O152.8[理学—数学]