On the Minimum Graphs Which Contain all Small Trees

Let \(E_n\) denote the minimum number of edges in a graph that contains every tree with \(n\) edges. This article provides two sets of data concerning \((n+1)\)-vertex graphs with \(E_n\) edges for each \(n \leq 11\): first, a minimum set of trees with \(n\) edges such that all trees with \(n\) edges are contained in such a graph whenever it contains the trees in the minimum set; second, all mutually nonisomorphic graphs that contain all trees with \(n\) edges.