论文标题
广义Gardiner-Praeger图及其对称性
Generalized Gardiner-Praeger graphs and their symmetries
论文作者
论文摘要
图形的自动形态组的子组在图上{\ em em half-aft-arc-transitationaly}，如果它在顶点集合和图表的边缘集上进行传输，而在图表集的弧线上不作用。如果图的完整自动形态组在半弧传递上起作用，则该图被称为{\ em em Half-arc-transitive}。 在1994年，Gardiner和Praeger介绍了两个四位弧电量的图表，称为$ c^{\ pm 1} $和$ c^{\ pm \ pm \ pm \ varepsilon} $图形，它们在与Arc-Transian compartian compartian compartian compartian compartian suplansian sualders and consutiation Aucormormormormorphisms的表征中起着重要作用商图是一个周期。所有的Gardiner-Praeger图都是弧线的，但承认一组半弧形的自动形态。最近，Poto \ v Cnik和Wilson介绍了CPM图，这是Gardiner-Praeger图的概括。这些图的大多数都是弧线的，但其中一些是半弧传递的。实际上，至少要订购$ 1000 $，每个四弧弧交易的奇数半径的松散图形大于$ 2 $的订单稳定器的奇数半径图是CPM图的同构。 在本文中，我们确定了CPM图的自动形态组，并研究了它们之间的同构。此外，我们确定哪些图是$ 2 $ -ARC的传输，它们是弧线传输的，但不是$ 2 $ -ARC的传输，哪些是半值传输的。
A subgroup of the automorphism group of a graph acts {\em half-arc-transitively} on the graph if it acts transitively on the vertex-set and on the edge-set of the graph but not on the arc-set of the graph. If the full automorphism group of the graph acts half-arc-transitively, the graph is said to be {\em half-arc-transitive}. In 1994 Gardiner and Praeger introduced two families of tetravalent arc-transitive graphs, called the $C^{\pm 1}$ and the $C^{\pm \varepsilon}$ graphs, that play a prominent role in the characterization of the tetravalent graphs admitting an arc-transitive group of automorphisms with a normal elementary abelian subgroup such that the corresponding quotient graph is a cycle. All of the Gardiner-Praeger graphs are arc-transitive but admit a half-arc-transitive group of automorphisms. Quite recently, Poto\v cnik and Wilson introduced the family of CPM graphs, which are generalizations of the Gardiner-Praeger graphs. Most of these graphs are arc-transitive, but some of them are half-arc-transitive. In fact, at least up to order $1000$, each tetravalent half-arc-transitive loosely-attached graph of odd radius having vertex-stabilizers of order greater than $2$ is isomorphic to a CPM graph. In this paper we determine the automorphism group of the CPM graphs and investigate isomorphisms between them. Moreover, we determine which of these graphs are $2$-arc-transitive, which are arc-transitive but not $2$-arc-transitive, and which are half-arc-transitive.
