Some Reduction Formulas and the Characterization of Singular and Nonsingular Directed Fans
S. Gervacio, l. Jose (pp. 34-38)
Abstract
A diagraph is called singular or nonsingular according as its adjacency matrix is singular or nonsingular. An expression of the determinant of the adjacency matrix of a diagrpah in terms of the determinant of smaller diagraphs obtained from the given one is called a reduction formula. Reduction formulas are established in this paper. Furthermore, using these reduction formulas, we determine which of the directed fan Fn is nonsingular, then the determinant of its adjacency matrix is (-1)n .