论文标题
在四载半弧度传递图上的围墙5
On tetravalent half-arc-transitive graphs of girth 5
论文作者
论文摘要
如果$ \ g $在$ \ g $上的操作在$ \ g $的顶点集上，并且在$ \ g $的边缘集上，则在$ \ g $上的{\ em Half-em half-g $ tho $ \ g $的自动形态组的子组在$ \ g $上是$ \ g $。周长$ 3 $和$ 4 $承认半弧透射式的自动形态的四甲图形图。在本文中，我们研究了周长$ 5 $的例子。我们表明，除两个例外，所有此类图仅针对边缘的相应诱导方向指导了$ 5 $ CYCLE。此外，我们分析了指示$ 5 $ CYCLE的示例，研究其一些图形理论属性，并证明此类图的$ 5 $ Cycles对于给定的半弧传递群体始终是一致的周期。我们还提供了无限的示例家族，对围墙的四款图表进行了分类，$ 5 $承认与它们紧密相关的半弧交易型自动形态，并对四弧的半弧度发行弱的弱元素进行分类。
A subgroup of the automorphism group of a graph $\G$ is said to be {\em half-arc-transitive} on $\G$ if its action on $\G$ is transitive on the vertex set of $\G$ and on the edge set of $\G$ but not on the arc set of $\G$. Tetravalent graphs of girths $3$ and $4$ admitting a half-arc-transitive group of automorphisms have previously been characterized. In this paper we study the examples of girth $5$. We show that, with two exceptions, all such graphs only have directed $5$-cycles with respect to the corresponding induced orientation of the edges. Moreover, we analyze the examples with directed $5$-cycles, study some of their graph theoretic properties and prove that the $5$-cycles of such graphs are always consistent cycles for the given half-arc-transitive group. We also provide infinite families of examples, classify the tetravalent graphs of girth $5$ admitting a half-arc-transitive group of automorphisms relative to which they are tightly-attached and classify the tetravalent half-arc-transitive weak metacirculants of girth $5$.
