 Full ternary tree

A rooted tree in which every internal vertex has exactly three tree children. For a finite rooted tree with $m$ tree leaves and internal outdegrees $d_v$, counting edges in two ways givesIndeed, the number of edges is the total number of vertices minus one and also the sum of the internal outdegrees. Thus a full ternary tree with $N$ internal vertices has $m=1+2N$ tree leaves, always an odd number. More generally, if every internal vertex has either two or three tree children, $m=1+N_2+2N_3$. This parity controls the initial merge in ternary Huffman coding.