Characterizations of some classes of strong sign nonsingular digraphs

Abstract

A square real matrix A is called a strong sign nonsingular matrix (or S 2NS matrix) if all the matrices with the same sign pattern as A are nonsingular and all the inverses of these matrices have the same sign pattern. The digraphs associated with S 2NS matrices are called S 2NS digraphs. In this paper, we give necessary and sufficient conditions in terms of the forbidden subdigraphs for some classes of digraphs to be S 2NS digraphs. These classes of digraphs are generalizations of the classes of digraphs studied in Brualdi and Shader (Matrices of sign-solvable linear system, Cambridge University Press, Cambridge, 1995) and Shao (Linear Algebra Appl. 282 (1998) 221–232).