Characterizations of some classes of strong sign nonsingular diagraphs

A square real matrix A is called a strong sign nonsingular matrix (or (SNS)-N-2 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 (SNS)-N-2 matrices are called (SNS)-N-2 digraphs In this paper, we give necessary and sufficient conditions in terms of the forbidden subdigraphs for some classes of digraphs to be (SNS)-N-2 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). (C) 2000 Elsevier Science B.V. All rights reserved.