The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $$h$$ is:

The maximum number of binary trees that can be formed with three unlabeled nodes is:

Consider a weighted complete graph $$G$$ on the vertex set $$\left\{ {{v_1},\,\,\,{v_2},....,\,\,\,{v_n}} \right\}$$ such that the weight of the edge $$\left( {{v_i},\,\,\,\,{v_j}} \right)$$ is $$2\left| {i - j} \right|$$. The weight of a minimum spanning tree of $$G$$ is

If all the edge weights of an undirected graph are positive, then any subject of edges that connects all the vertices and has minimum total weight is a