符号有向图的最大SNS-符号模式矩阵

摘要

For an asymmetric sign pattern matrix P , we analyze the sign characteristic of P with the help of a signed digraph in this paper. The maximal SNS-pattern matrix for a signed digraph is the maximal sign-nonsingular sub-pattern among all real matrices having the given sign pattern P . In this paper, SNS problems for signed digraphs are studied by converting a signed digraphΓinto a signed bipartite graph G(U, V ). We propose the algorithms for searching for a sub-signed bipartite graph G(U′, V′) with the maximum perfect matching M′ corresponding to every set of disjoint M′-interlacing cycles, which contain an even number of M′-interlacing e-cycles. The maximal SNS-pattern for a signed digraph is obtained according to algorithms.%对于非对称符号模式矩阵P，可借助于符号有向图来分析符号模式矩阵P的符号特征。符号有向图的最大SNS-符号模式矩阵是非对称符号模式矩阵P的最大非奇矩阵。符号二部图为研究符号有向图的最大SNS-符号模式矩阵和最小秩提供了一个新的途径。本文将符号有向图转换为符号二部图G(U, V )，并提出了构造G(U, V )的最大子图的算法：一是在G(U′, V′)中寻求最大完美匹配M′；二是寻求含有偶数个e-圈且不相交的M′-交替圈。通过算法而构造了符号有向图的SNS-符号模式矩阵。