T with p internal vertices such that the sum of all the color numbers of T is n− 2p. DefineTn =Sp=0Tn,p. Let Bn denote the set of complete binary trees with n internal vertices.For any B ∈ Bn, let P = v1v2 · · · vk be a path of length k of B (viewed from the root ofB). P is called a R-path, if (1) viis the right child of vi− 1 for 2 6 i 6 k and (2) the leftchild of vi is a leaf for 1 6 i 6 k. In addition, P is called a maximal R-path if there existsno vertex u such that uP or P u forms a R-path. P is called an L-path, if k > 2 and vi isthe left child of vi− 1 for 2 6 i 6 k. P is called a maximal L-path if there exists no vertexu such that uP or P u forms an L-path. Clearly,...