On the inverse of bipartite graphs with unique perfect matchings and reciprocal eigenvalue properties

Abstract

The study of graph structures via different properties of its adjacency matrix is a widely studied subjects Sometimes different structural properties of a graph get characterized by different properties of the eigenvalues and the eigenvectors of the associated adjacency matrix For example it is well known that 732 a simple graph G is connected if and only if G spectral radius is a simple eigenvalue with an eigenvector whose coordinates are nonzero and of the same sign 8482 There are many