二面体群的中心图(英文)

The Center Graphs on Dihedral Groups

设Γ是个非交换群且Ω是Γ的一个子集.中心图G(Γ,Ω)以Ω作为它的顶点,如果对于Γ的两个不同的顶点a,b有ab∈Z(Γ),则它们相连.该文讨论建立在二面体群D2n关于某些子集上的中心图的某些性质.特别地,该文获得了某些中心图G(D2n,Ω)的着色数和团数.

Let Γ be a non-abelian group and Ω■Γ.The center graph G（Γ,Ω） has Ω as its vertex set with two distinct elements a,b of Ω which are adjacent if and only if ab∈Z（Γ）,where Z（Γ） is the center of Γ.In this paper we discuss certain properties of center graphs constructed on the dihedral group D2n with respect to some specific subsets of D2n.More specifically we obtain the chromatic number and clique number of G（D2n,D2n）.