回路1、2-弦图的逆M矩阵完备及其算法设计

对已定元均不为零的部分逆M矩阵,通过变换使其对角线上元素均为1后,根据其所对应图形的特点,得到结果如下:(a)若其所对应图形为简单有向回路或回路1-弦图,具有逆M矩阵完备式当且仅当所有简单有向回路的回路积均小于1.(b)若其所对应图形为回路2-弦图,具有逆M矩阵完备式当所有简单有向回路满足回路积小于1,且对其中依次在两个顶点处相交的有向回路标明层次后,任一有向回路的回路积均小于与其相连接的上一层的有向回路的回路积.

INVERSE M-MATRICES COMPLETIONS OF THE CYCLIC 1,2-CHORDAL DIGRAPH AND THE ALGORITHM DESIGN

For a partial inverse M-matrix which has no zero entries,after making all diagonal entries of it be equal to 1 by transformation,according to the characteristic of its digraph we obtain the results as follows:(a)the digraph associated to it is a simple directed cycle or cyclic 1-chordal digraph and it has an inverse M-matrix completion if and only if the gain on any simple directed cycle in it is less than 1.(b)the digraph associated to it is a cyclic 2-chordal digraph and it has an inverse M-matrix completion if the gain on any simple cycle in it is less than 1 and after marking the level of the directed cycles sequentially intersecting at two vertices,the gain on any directed cycle is less than the gain on the cycle connected with it in the level above.