The Singularity of Bipartite Graph

Abstract

A graph
is said to be singular if and only if its adjacency matrix is singular. A graph
is said to be bipartite graph if and only if we can write its vertex set as
, and each edge has exactly one end point in
and other end point in
. In this work, we will use graphic permutation to find the determinant of adjacency matrix of bipartite graph. After that, we will determine the conditions that the bipartite graph is singular or non-singular.