关于图的谱半径的一个改进上界

通过对图的邻接矩阵结构的分析和讨论，得到了一个关于图的谱半径的一个新的上界，从而改进的几个已知的结果。     

关于二次线性迭代序列的一些恒等式

利用形式幂级数的变换技巧，得到了一类关于二次线性迭代序列的恒等式。特别地，可选择恒等式中所涉及的参变量，以得到关于古典Ｆｉｂｏｎａｃｃｉ数和Ｌｕｃａｓ数的倒数幂的恒等式。     

和图、整和图与模和图的几个结果

Let N denote the set of positive integers. The sum graph G^＋（S） of a finite subset S belong to N is the graph （S, E） with uv ∈ E if and only if u ＋ v ∈ S. A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S belong to N. By using the set Z of all integers instead of N, we obtain the definition of the integral sum graph. A graph G = （V, E） is a mod sum graph if there exists a positive integer z and a labelling, λ, of the vertices of G with distinct elements from {0, 1, 2,..., z - 1} so that uv ∈ E if and only if the sum, modulo z, of the labels assigned to u and v is the label of a vertex of G. In this paper, we prove that flower tree is integral sum graph. We prove that Dutch m-wind-mill （Dm） is integral sum graph and mod sum graph, and give the sum number of Dm.     

和图、整和图及模和图的几个结果

Let N denote the set of positive integers.The sum graph G (S) of a finite subset S (C) N is the graph (S,E) with uv ∈ E if and only if u v ∈ S.A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S С N.By using the set Z of all integers instead of N,we obtain the definition of the integral sum graph.A graph G=(V,E) is a mod sum graph if there exists a positive integer z and a labelling,λ,of the vertices of G with distinct elements from {0,1,2,...,z-1} so that uv ∈ E if and only if the sum,modulo z,of the labels assigned to u and v is the label of a vertex of G.In this paper,we prove that flower tree is integral sum graph.We prove that Dutch m-wind-mill (Dm) is integral sum graph and mod sum graph,and give the sum number of Dm.     

关于广义Stirling数偶的同余性

本文证明了广义Ｓｔｉｒｌｉｎｇ数偶的一些同余性质，从而回答了文［５］中的一个猜测．这些结果做为特例推广了已知的关于两类Ｓｔｉｒｌｉｎｇ数的同余性质．     

组合数的一种矩阵表示及应用

给出由一对恰当的指数型发生函数所确定的无穷矩阵表示二元组合序列的方法．通过发生函数的代数运算，可用于统一处理一些涉及二项式系数及Ｓｔｉｒｌｉｎｇ型数偶的组合恒等式．最后，给出这种无穷矩阵的同余性刻划     

两对加权Stirling数偶及其性质

从非中心变步长差与正常差分之间的转换关系出发，导出两对加权型Ｓｔｉｒｌｉｎｇ数偶并讨论了它们的性质，所得结果是Ｃａｒｌｉｔｚ及Ｈｏｗａｒｄ分别讨论了退化Ｓｉｒｌｉｎｇ数的直交扩展，并可用于生成一类反演关系。