Topological classification of binary trees using the Horton-Strahler index
نویسندگان
چکیده
منابع مشابه
A Note on the Horton-Strahler Number for Random Trees
We consider the Horton-Strahler number S, for random equiprobable binary trees with n nodes. We give a simple probabilistic proof of the well-known result that ES, = log,n + O(1) and show that for every x > 0, P{ 1 S, log,n ( > x} Q D/4x, for some constant D > 0.
متن کاملOn the Horton-Strahler Number for Random Tries
We consider random tries constructedfrom n i.i.d. séquences of independent Bernoulli (p) random variables, 0 < p < 1. We study the Horton-Strahler number Hn, and show that ëmin(p,l-p) in probability as n —*• oo.
متن کاملA bijection from ordered trees to binary trees that sends the pruning order to the strahler number
It is well known (e.g. [3], p. 60) that the number of ordered trees with n vertices equals the number of complete binary trees with n leaves. Vauchaussade de Chaumont and Viennot [4,6] ( see also [3], ch. 3, ex. 6 (p. 103)) discovered an interesting refinement of this fact. They proved that for any integers n and k, the number of ordered trees with IZ vertices and pruning order k equals the num...
متن کاملHorton Law in Self-Similar Trees
Abstract. Self-similarity of random trees is related to the operation of pruning. Pruning R cuts the leaves and their parental edges and removes the resulting chains of degree-two nodes from a finite tree. A Horton-Strahler order of a vertex v and its parental edge is defined as the minimal number of prunings necessary to eliminate the subtree rooted at v. A branch is a group of neighboring ver...
متن کاملOn the forgotten topological index
The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2001
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.65.016130