DETERMINANTS, PERMANENTS AND BIPARTITE GRAPHS,

The combinatorial properties of a nonnegative matrix M are captured by that binary matrix A AM in which the entries are 1 whenever those of M are positive. If A is a square matrix, then it can be regarded as the adjacency matrix of a directed graph digraph. If A is rectangular, a bipartite graph bigraph can be associated with A of course this can also be done for A square. The determinant of the adjacency matrix of a graph or digraph has been expressed in terms of its structure, and so has the permanent. The purposes of this report are to express the permanent of a square or rectangular binary matrix in terms of the associated bigraph, and to formulate the determinant of a square matrix in terms of its bigraph. Author