一类混合图的结构及其特征空间

主要讨论具有如下性质的一类连通混合图G:其所有非奇异圈恰有一条公共边,且除了该公共边的端点外,任意两个非奇异圈没有其它交点.本文给出了图G的结构性质,建立了其最小特征值λ1(G)(以及相对应的特征向量)与某个简单图的代数连通度(以及Fiedler向量)之间联系,并应用上述联系证明了λ1(■)≤α(G),其中G是由G通过对其所有无向边定向而获得,α(■)为■的代数连通度.     

Spectral properties of Pascal graphs

We obtain spectral properties of the Pascal graphs by exploring its spectral graph invariants such as the algebraic connectivity, the first three largest Laplacian eigenvalues and the nullity. Some open problems pertaining to the Pascal graphs are given.     

On the Kirchhoff index of some toroidal lattices

The resistance distance is a novel distance function on a graph proposed by Klein and Randi? [D.J. Klein and M. Randi?, Resistance distance, J. Math. Chem. 12 (1993), pp. 81–85]. The Kirchhoff index of a graph G is defined as the sum of resistance distances between all pairs of vertices of G. In this article, based on the result by Gutman and Mohar [I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996), pp. 982–985], we compute the Kirchhoff index of the square, 8.8.4, hexagonal and triangular lattices, respectively.     

Ordering Trees with Nearly Perfect Matchings by Algebraic Connectivity

Let T2k＋1 be the set of trees on 2k＋1 vertices with nearly perfect matchings and α（T） be the algebraic connectivity of a tree T. The authors determine the largest twelve values of the algebraic connectivity of the trees in T2k＋1. Specifically, 10 trees T2,T3,... ,T11 and two classes of trees T（1） and T（12） in T2k＋1 are introduced. It is shown in this paper that for each tree T^′1,T^″1∈T（1）and T^′12,T^″12∈T（12） and each i,j with 2≤i〈j≤11,α（T^′1）=α（T^″1）〉α（Tj）〉α（T^′12）=α（T^″12）.It is also shown that for each tree T with T∈T2k＋1／（T（1）∪{T2,T3,…,T11}∪T（12））,α（T^′12）〉α（T）.     

图的Laplacian特征值

本文研究了连通图的Laplacian特征值,利用图的Laplacian矩阵的特征多项式的行列式表示式,对存在两个不同顶点,但有相同邻集的一类图,得到了一个Laplacian特征值,并给出了它的应用.     

A relative bound for independence

We prove an upper bound for the independence number of a graph in terms of the largest Laplacian eigenvalue, and of a certain induced subgraph. Our bound is a refinement of a well-known Hoffman-type bound.     

Laplace特征值的一点注记

确定具有n个顶点e条边的图的Laplace的最大谱半径.     

双圈图的Laplacian Spread(英文)

Laplacian spread的概念在刻画图的整体性质方面非常重要.近年来,Fan等分别刻画了树中具有极大和极小Laplacian spread的图.另外Bao等确定了在所有单圈图中具有极大Laplacian spread的图.边数减去顶点数目为1的连通图称为双圈图.令B_n是所有有n个顶点构成的双圈图集合.对n≥11,本文确定了B_n中所有具有极大Laplacian spread的那些图.     

一类苯环的Kirchhoff指标（英文）

如果用单位电阻来代替图G中的每条边得到一个电网络,而顶点i和j之间的电阻距离（Resistance distance）定义为此网络中节点i和j之间的等效电阻的阻值.图G的Kirchhoff指标定义为G中所有点对之间的电阻距离和.本文利用循环矩阵的理论得到了一类苯环R_n的Kirchhoff指标的计算公式,而且我们证明了R_n的Kirchhoff指标渐近等于R_n的Wiener指标的一半.