An application of graph theory to determinants

This thesis presents how Coates and Konig digraphs were applied to determinants. Each of these digraphs can be used to represent an n x n matrix. The Coates digraph has n vertices corresponding to the number of rows (columns) of a matrix and the arcs drawn from vertex i to vertex j where the label of the arc is the entry aij of the matrix. The Konig digraph on the other hand has m + n vertices, m corresponds to the rows and n corresponds to the columns of the matrix. The row vertices are labelled from l to m and the column vertices, from l to n and are arranged in increasing order from top to bottom.Most of the theorems are about the properties of the determinants while the other theorems show the relationship or similarities of the two digraphs and its counterpart in the usual method of finding the determinants