Riordan有向图

Riordan digraphs

为了拓展Riordan阵与Riordan群理论,提出Riordan有向图的概念并研究其性质,由此建立整数序列、Riordan阵与图之间的联系。首先,基于Riordan阵,定义Riordan有向图,并利用Riordan阵的基本性质得到Riordan有向图的边集满足的条件。然后,给出Riordan有向图含有Hamilton路的一个充分条件以及Riordan有向图是本原有向图的一个充分条件。最后,通过Riordan群上的对角平移算子提出构造同构Riordan有向图的方法。结果表明:一些特殊的整数序列与有向图之间有良好的对应,且利用Riordan阵理论可以将一些整数序列的性质反映到有向图的性质上。

In order to expand the theory of Riordan arrays and Riordan group, we introduce the concept of Riordan digraphs and study their properties. As a result, we establish the relations among integer sequences, Riordan arrays and graphs. Firstly, we define the Riordan digraphs on the basis of Riordan arrays, and obtain the conditions of the edge-sets of the Riordan digraphs by using the basic properties of Riordan arrays. Next, we conclude a sufficient condition for the existence of a Hamilton path in a Riordan digraph and a sufficient condition for a Riordan digraph to be primitive. Finally, we propose a method to construct isomorphic Riordan digraphs by using diagonal translation operator on the Riordan group. The results show that some special integer sequences are well related to digraphs, and some properties of integer sequences can be reflected to those of digraphs by using the theory of Riordan arrays.