Accession Number : AD0669561

Title :   DETERMINANTS, PERMANENTS AND BIPARTITE GRAPHS,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Harary,Frank

Report Date : MAY 1968

Pagination or Media Count : 10

Abstract : The combinatorial properties of a nonnegative matrix M are captured by that binary matrix A = A(M) 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)

Descriptors :   (*GRAPHICS, *MATRICES(MATHEMATICS)), (*COMBINATORIAL ANALYSIS, MATRICES(MATHEMATICS)), PERMUTATIONS, DETERMINANTS(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE