The generating graph of a finite group G is defined as the graph with vertex set G such that \(x,y\in G\) are adjacent if and only if they generate G. In this paper, we investigate some graph theoretic properties of the generating graphs of certain solvable groups, and the influence of generating graph on the structure of a group. In particular, we show that for a square-free integer m, the dihedral group of order 2m is uniquely determined by its generating graph, and if further m is odd then the generalized quaternion group of order 4m is uniquely determined by its generating graph. We also present some examples of nonisomorphic groups which have isomorphic generating graphs.
