分支数≤7时S^2NS有向图的禁用子图刻划

The Characterizations of S^2NS Digraphs with the Number of Components ≤ 7 in Terms of Forbidden Configurations

实方阵A称为强符号非异阵（S^2NS阵）,若任一与A符号模式相同的矩阵非异且其逆的符号模式也一致。若一个有向图是某一S^2NS阵对应赋号有向图的基础有向图,称为S^2NS有向图。本文用禁用子图形式给出了分支数≤7时有向图成为S^2NS有向图的刻划,同时部分地解决了[2]和[4]中提出的问题。

A square real matrix is called a strong sign nonsingular matrix (S2NS matrix) if all matrices with the same sign pattern as A are nonsingular and the inverses of these matrices all have the same sign pattern. A digraph which is the underlying digraph of an S2NS matrix (with negative main diagonals) is called an S2NS digraph. In this paper we give the characterizations for S2NS digraph when the numbers of their components(?) 7 in terms of forbidden configurations and obtain some answers to the open problems in [2] and [4].