All of Graphs of the Platonic Solids are Graceful

The term"graceful graph"was proposed by Professor S.W.Golomb in Southen Califor-nia University in 1972[1].A question arisen in reference [1] is answered in this article. Let G be a simple graph of γ vertices and εedges.G is graceful if there is a labelling l ofits vertices with distinct integers from the set{0,1,…,ε},so that the induced edge labellingl’defined by     

A Graceful Algorithm of a Class of Trees

Let T be a tree with v vertices. It is said to be graceful if we can label the vertices with numbers 1,2,……,v in such a manner that the differences of any two adjacent vertices will again form the set {1,2,…,v-1}.Ringel conjectured, in1963, that every tree has a such labelling [1]. Ringel's conjecture remains unsettled. In this article, we shall investigate a class of graceful trees. Definition The,T_λ~((n)) is a tree with v_n vertices. Its vertices are v_i(j=0,1,…,n+1);v_(?)(j_o=1,2,…,n;j_1=1,2,…,k_1;……; j=1,2,…,k,≤λ), where λ,n,k_1,     

聚省分子轨道的差分方程法

由于聚省分子中的原子可以分成两类原子团轨道,即A和B,以从左到右的次序进行编号,并用字母q表示某个原子的编号,将轨道系数C看作原子编号的函数,称为载波^[1],分别记为a_q(q=1,2,…,n),b_q(q=1,2,…,n+1)。     

关于四位数和三位数的K变换黑洞

关于四位数和三位数的Ｋ变换黑洞李鸿样（上海铁道学院，本刊通讯编委）戴宏图（上海宝山区北余大学）编者按：由于本刊１９９４年第６期文［２］末尾未给出文献，在审稿时没有核对原文，至使对原文的意思理解不准确而造成失误．此文正好可以提供给读者一个准确的理解．我...