Many Sub Trees k Dots from the Tree Where the Degrees of the Points are Known

EasyChair Preprint 4988

Abstract

Let S and T be trees with | S | = k. The notation c (S, T) is the number of copies of S in T. The number of subtrees of T with the number of k points and the meaning of the number of copies of S in T are important elements in determining the profile of the tree locally. Let d = (d0, d1, d2, ..., dn) be an ascending sequence of degrees to all points on the tree. The set of trees whose degree of points corresponds to d is denoted by Td. A Td tree * that corresponds to d and has the maximum number of subtrees with k points can be constructed. The first step is to assign the point corresponding to degrees d0 as the root of the tree. The total s1 = d0 points on the first level are the points corresponding to the next term d0 in the degree sequence. A total of s2 = d2 + d3 + ... + - s1 points on the second level which correspond to as many as s2 of the next term in the degree sequence. For points on the third level and so on, it is done the same as at the second level. Tree is a tree that has the most number of sub-trees with the highest k points of all trees at Td.

Keyphrases: optimal trees, profiles, trees, well-ordering

@booklet{EasyChair:4988,
  author    = {Efron Manik},
  title     = {Many Sub Trees k Dots from the Tree Where the Degrees of the Points are Known},
  howpublished = {EasyChair Preprint 4988},
  year      = {EasyChair, 2021}}