论文标题
改进的Moore绑定和一些新的最佳Abelian Cayley图表
An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs
论文作者
论文摘要
我们认为混合图（有针对性边缘和无方向的边缘）的情况是Abelian组的Cayley图。在这种情况下，对于此类图可以达到的最大顶点数量，得出了一些摩尔边界。如果我们知道有关生成集的某些元素的更多详细信息，我们首先显示这些界限可以得到改善。基于这些改进，我们介绍了一些新的混合图。对于该程度的每个固定值，这些家族随着直径的增加而具有渐近数量的顶点。在某些情况下，获得的结果被证明是最佳的。
We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first show these bounds can be improved if we know more details about the order of some elements of the generating set. Based on these improvements, we present some new families of mixed graphs. For every fixed value of the degree, these families have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.
