Characterizations of some classes of strong sign nonsingular digraphs Original Research Article

A square real matrix A is called a strong sign nonsingular matrix (or S2NS 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 S2NS matrices are called S2NS digraphs. In this paper, we give necessary and sufficient conditions in terms of the forbidden subdigraphs for some classes of digraphs to be S2NS 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).