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In a graph  G , if  d iis the degree of a vertex  v i, the geometric-arithmetic matrix  GA ( G ) is a square matrix whose-th entry iswhenever 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 spreadof  G . In this article, we investigate some properties ofWe obtain lower and upper bounds ofand show the existence of graphs for which equality holds. Further,is computed for various graph operations.

On the spread of the geometric-arithmetic matrix of graphs