论文标题
在有向图中计数路径
Counting paths in directed graphs
论文作者
论文摘要
我们考虑具有$ n \ geq 1 $边缘的定向图类别，并且没有循环短于$ k $。使用标记图的概念，我们确定此类的图形，以最大程度地增加$ k $的所有路径的数量。然后，我们显示了该结果的$ r $标签版本，该版本对于非负实际数字的半度性$ r $包含，并包含非负合理数字的半度。最后，我们提出了一个相关的开放问题，该问题与$ n \ geq1 $边缘的无环图的路径代数的最大维度有关。
We consider the class of directed graphs with $N\geq 1$ edges and without loops shorter than $k$. Using the concept of a labelled graph, we determine graphs from this class that maximize the number of all paths of length $k$. Then we show an $R$-labelled version of this result for semirings $R$ contained in the semiring of non-negative real numbers and containing the semiring of non-negative rational numbers. We end by posing a related open problem concerning the maximal dimension of the path algebra of an acyclic graph with $N\geq1$ edges.
