优美树的生长

Growth of Graceful Trees

给出了优美树的一种生长方法。设Ｔ是一棵优美树，从Ｔ的每个顶点都长出一棵优美树，则只要满足下列条件，这棵新树Ｔ＇仍是优美树：１）对每个顶点ｕ∈Ｖ（Ｔ），在ｕ点长出一棵优美标号为的优美树Ｒ＿ｕ，且｜Ｖ（Ｒ＿ｕ）｜＝ｎ（ｎ∈｛１，２，…｝），２）对每个顶点ｕ∈Ｖ（Ｔ），有Ｒ＿ｕ＝Ｒ＿ｕ－，且ｕ和为Ｒ＿ｕ和Ｒ＿ｕ－的同构点，当Ｒ＿ｕ是由一棵星形树及一条路组成，以及每个Ｒ＿ｕ都是相同的优美树情形时优美树的生长方法，已有证明。本文在此基础上推广了其生长范围。

A method for the graceful tree to grow is given:If T is a graceful tree,every vertex from the tree grows a graceful tree,so a new tree called T' is given. The new tree is still graceful tree if the following conditions are satisfied; 1) For every u∈V(T) ,a gracefultree R_u in graceful labelling grows on it, and |V (R_u)|= n(n∈{1, 2,...}), 2) For every u∈V(T), R_u= R-_u and the vertex u is isomorphic point of R_u and u is isomorphic paint of R-_u The method for the graceful tree to grow when R_u is composed of a radial tree and a path and every R_u is the same graceful tree that has been given. On the basis of that the range of the growth of the graceful tree has been extended.