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arXiv 1504.006452015-04-02math.CO

某些有限非阿贝尔群的子群可置换图

Permutability graphs of subgroups of some finite non-abelian groups

R. Rajkumar, P. Devi

备注：: 35 pages, 1 figure
DOI：: 10.1142/S1793830916500476

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AI总结：

本文研究二面体群、广义四元数群、拟二面体群和模群的子群可置换图结构，并系统考察其边数、度数、独立数、支配数、团数、色数、弱完美性、欧拉性和哈密顿性等图论参数。

摘要：

本文研究以下群的子群可置换图及非正规子群可置换图的结构：二面体群 $D_n$、广义四元数群 $Q_n$、拟二面体群 $QD_{2^n}$ 和模群 $M_{p^n}$。进一步，我们考察这些图的边数、顶点度数、独立数、支配数、团数、色数、弱完美性、欧拉性和哈密顿性。

英文摘要：

In this paper, we study the structure of the permutability graphs of subgroups, and the permutability graphs of non-normal subgroups of the following groups: the dihedral groups $D_n$, the generalized quaternion groups $Q_n$, the quasi-dihedral groups $QD_{2^n}$ and the modular groups $M_{p^n}$. Further, we investigate the number of edges, degrees of the vertices, independence number, dominating number, clique number, chromatic number, weakly perfectness, Eulerianness, Hamiltonicity of these graphs.

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