广义Petersen图和Kronecker盖

Discret. Math. Theor. Comput. Sci. Pub Date : 2019-11-11 DOI:10.23638/DMTCS-21-4-15

Matjaž Krnc, T. Pisanski

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引用次数: 3

摘要

广义Petersen图族$G(n,k)$由Coxeter等人[4]引入，由Mark Watkins(1969)命名，它是由正多边形的顶点与星形多边形的相应顶点连接而成的三次图族。简单无向图$G$的Kronecker覆盖$KC(G)$是$G$的二部覆盖图的一种特殊类型，它同构于$G$与$K_2$的直接张量积。我们刻画了广义Petersen图的Kronecker覆盖的所有成员，并描述了它们各自商的结构。我们观察到一些这样的商是再次广义的Petersen图，并描述了所有这样的对。本文的结果已在EUROCOMB 2019上发表，扩展摘要已在其他地方发表。

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Generalized Petersen graphs and Kronecker covers

The family of generalized Petersen graphs $G(n,k)$, introduced by Coxeter et al. [4] and named by Mark Watkins (1969), is a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. The Kronecker cover $KC(G)$ of a simple undirected graph $G$ is a a special type of bipartite covering graph of $G$, isomorphic to the direct (tensor) product of $G$ and $K_2$. We characterize all the members of generalized Petersen graphs that are Kronecker covers, and describe the structure of their respective quotients. We observe that some of such quotients are again generalized Petersen graphs, and describe all such pairs.The results of this paper have been presented at EUROCOMB 2019 and an extended abstract has been published elsewhere.

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来源期刊

Discret. Math. Theor. Comput. Sci.

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