Seminar

Abstract
In Combinatorial Matrix Theory, the study of graph structures via dif- ferent properties of matrices associated with it is an interesting and popular topic. Among the various matrices associated with a graph, the adjacency matrix is probably the most popular and widely investigated one.
A graph G is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G, when it exists, is the unique weighted graph whose adjacency matrix is signature similar to A(G)−1. The inverse graph of an invertible graph G is denoted by G+. A nonsingular graph G satisfies reciprocal eigenvalue property or property R if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and G satisfies strong reciprocal eigenvalue property or property SR if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and they both have the same multiplicities. In many ways these two concepts are related to each other. Both of these play important roles in Quantum Chemistry. In this talk, we will study the graph structure with regard to the concepts inverse graph and reciprocal eigenvalue properties.