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

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.