Showing papers on "Binary tree published in 1970"

On the Number of Subtrees of a Symmetric n-Ary Tree

Abstract: Expressions for the number of nonisomorphic rooted subtrees of an n-ary rth generation symmetric tree given both recursively in r and asymptotically in r are developed, along with a closed form expression in r for each fixed n. Similar results are obtained for two other cases with the respective additional constraints: (i) all subtrees must have a radius of r, (ii) all nonterminal vertices of each subtree must branch to exactly n other vertices of the subtree farther from the root. Some numerical results are given from which it is shown that amongst the symmetric n-ary trees the binary trees have the greatest rate of growth of the number of nonisomorphic subtrees in terms of the number of vertices of the tree.