有向圈的行列式算法及HAMILTON图条件

Determinant Calculation of Directed Cycles andCondition for Hamilton Digraph

本文引入有向路乘法、弧行列式等概念 ,讨论了弧行列式的性质 ,阐述了二种计算有向圈的行列式方法及有向图 D为 Hamilton图的充要条件 。

In this paper, several definitions are provided, such as the multiplication of directed path, arc determinant and so on. Some fundamental qualities of arc determinant are discussed and two determinant approaches to calculating the directed cycles of the digraph are expounded. One necessary and sufficient condition for a digraph to be a Hamilton digraph is put forward. Finally, a case is discussed.