On the spread of the geometric-arithmetic matrix of graphs

In a graph G, if d_i is the degree of a vertex v_i, the geometric-arithmetic matrix GA(G) is a square matrix whose (Formula presented.) -th entry is (Formula presented.) whenever vertices i and j are adjacent and 0 otherwise. The set of all eigenvalues of GA(G) including multiplicities is known as the geometric-arithmetic spectrum of G. The difference between the largest and the smallest geometric-arithmetic eigenvalue is called the geometric-arithmetic spread (Formula presented.) of G. In this article, we investigate some properties of (Formula presented.) We obtain lower and upper bounds of (Formula presented.) and show the existence of graphs for which equality holds. Further, (Formula presented.) is computed for various graph operations.