Graffiti的三个猜想

ON THE THREE CONJECTURES OF GRAFFITI

本文证明了当树 T 的|V(T)|≥3时,T 的每个点平均度的倒数和 I_d(T)与其半径 R(T)满足1/3≤I_d(T)—R(T),并举例否定了第579及第580两个猜想。

In this paper,the 577th Graffiti's conjecture(Let T be a tree with at least three vertices,I_(?)(T) be the sum of the inverse of the average degree for the all vertices and R(T) be the radium of T.Then 1/3≤I_(?)(T)-R(T).At the same times,give out infinite counter xamples for the 579th and 580th Graf- fiti's conjectures.