On the spread of the geometric-arithmetic matrix of graphs

In a graph G, if di is the degree of vertex vi, geometric-arithmetic matrix GA(G) square whose (i,j)-th entry 2didjdi+dj whenever vertices i and j are adjacent 0 otherwise. The set all eigenvalues including multiplicities known as spectrum G. difference between largest smallest eigenvalue called spread SGA(G) this article, we investigate some properties SGA(G). We obtain lower upper bounds show existence graphs for which equality holds. Further, computed various operations.