中文摘要：

简单有向图D（无环与重弧）,如果满足每个最小点割都是某个点的出邻点集或入邻点集,则称D是超连通的.在超连通有向图D中,如果存在一个最小点割既是某个点的出邻点集又是某个点的入邻点集,则称D是双超连通的.主要研究了线图双超连通性的充要条件;同时,研究了笛卡尔积与字典积的双超连通性.

英文摘要：

A simple digraph D（without loops and multiple arcs） is said to be superconnected if every minimum vertex-cut is the out-neighbor set or in-neighbor set of a vertex.A super-connected digraph D is said to be bi-super-connected if there exists a minimum vertex-cut is both the out-neighbor set of a vertex and the in-neighbor set of a vertex.In this paper,we will give the necessary and sufficient conditions of line digraph is bisuper-connected,furthermore,we study the bi-super-connectivity of Cartesian product and lexicographic product of two digraphs.