vertex with no direct successors, and the average branching factor of a game tree is the average outdegree of the graph. Combinatorial enumeration The number of rooted undirected graphs for 1, 2, ... nodes is 1, 2, 6, 20, 90, 544, ... Related concepts A special case of interest are rooted trees, the trees with a distinguished root vertex. If the directed paths from the root in the rooted digraph are additionally restricted to be unique, then the notion obtained is that of (rooted) arborescence—the directed-graph equivalent of a rooted tree. A rooted graph contains an arborescence with the same root if and only if the whole graph can be reached from the root, and computer scientists have studied algorithmic problems of finding optimal arborescences. Rooted graphs may be combined using the rooted product of graphs. See also k-vertex-connected graph pointed set References Further reading External links Extensions and generalizations of graphs