On Wiener‐type polynomials of thorn graphs

We derive the expressions of the ordinary, the vertex‐weighted and the doubly vertex‐weighted Wiener polynomials of a type of thorn graph, for which the number of pendant edges attached to any vertex of the underlying parent graph is a linear function of its degree. We also define variable vertex‐weighted Wiener polynomials and calculate them for the same type of thorn graphs. Copyright © 2009 John Wiley & Sons, Ltd.     

图的谱矩序列与图的排序

图的谱矩是代数图论中一个重要的代数不变量,本文通过计算图的第5、6阶谱矩,研究了图的结构与图的谱矩之阃的联系,动态地研究了图的结构变化(包括图的阶数的增大及同阶前提下所含圈长度的变化等)对谱矩序列排列的影响,给出了研究图依谱矩序列排序问题的新方法.     

Curvature notions on graphs

We survey some geometric and analytic results under the assumptions of combinatorial curvature bounds for planar/semiplanar graphs and curvature dimension conditions for general graphs.     

不含偶圈双圈图的极小斜能量

令G为简单连通图. 给图G的每条边赋予一个方向, 得到的有向图, 记为G^\sigma. 有向图G^\sigma的斜能量E_{s}(G^{\sigma})定义为G^\sigma的斜邻接矩阵特征值的绝对值之和. 令\mathcal{B}^\circ_{n}表示顶点个数为n不含偶圈的双圈图的集合. 考虑了\mathcal{B}^\circ_{n}中图依斜能量从小到大的排序问题. 利用有向图斜能量的积分公式和实分析的方法, 当n \geq 156和155 \geq n\geq 12时, 分别得到了\mathcal{B}^\circ_{n}中具有最小、次二小和次三小斜能量的双圈图.     

两类广义控制问题的NP-完全性

研究两类广义控制问题的复杂性: k-步长控制问题和k-距离控制问题, 证明了k-步长控制问题在弦图和平面二部图上都是NP-完全的. 作为上述结果的推论, 给出了k-距离控制问题在弦图和二部图上NP-完全性的新的证明, 并进一步证明了k-距离控制问题在平面二部图上也是NP-完全的.     

一类Catley图的Vosperian性质

设Sn是对称群,S是Sn中一些奇置换共轭类的并,在本文中,证明了Cayley图C（Sn,S)是Vosperian的,除非它是完全二部图。     

Topological Constructions in the o–Graph Calculus

Benedetti and Petronio developed in [1] a so called o–Graph Calculus, where a compact oriented 3–manifold with nonempty boundary could be described by a quadrivalent graph together with some extra structure. In this paper, we will show how topological constructions such as puncturing, connected sums, attaching handles, closing boundary components and product and mapping tori constructions can be translated into the o–graph calculus.     

Oriented list colorings of graphs

A 2‐assignment on a graph G = (V,E) is a collection of pairs L(v) of allowed colors specified for all vertices v ∈V. The graph G (with at least one edge) is said to have oriented choice number 2 if it admits an orientation which satisfies the following property: For every 2‐assignment there exists a choice c(v)∈L(v) for all v ∈V such that (i) if c(v) = c(w), then vw ∉ E, and (ii) for every ordered pair (a,b) of colors, if some edge oriented from color a to color b occurs, then no edge is oriented from color b to color a. In this paper we characterize the following subclasses of graphs of oriented choice number 2: matchings; connected graphs; graphs containing at least one cycle. In particular, the first result (which implies that the matching with 11 edges has oriented choice number 2) proves a conjecture of Sali and Simonyi. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 217–229, 2001     

化学单圈图的原子键连通性指数

图G的原子键连通性指数的定义如下:ABC(G)=∑uv∈E(G)((du+dv-2)dudv)(1/2).其中du、dv分别表示图G的边uv的2个端点u、v的度数.ABC指数已被证实为研究烷烃的稳定性以及环烷烃的应变能提供了一个很好的模型.讨论了n阶化学单圈图,给出了其ABC指数的可达的下界及其相应的极图     

Closure and stable Hamiltonian properties in claw‐free graphs

In the class of k‐connected claw‐free graphs, we study the stability of some Hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these properties there is an infinite family of graphs G_k of arbitrarily high connectivity k such that the closure of G_k has the property while the graph G_k does not); (ii) traceability is a stable property even for k = 1; (iii) homogeneous traceability is not stable for k = 2 (although it is stable for k = 7). The article is concluded with several open questions concerning stability of homogeneous traceability and Hamiltonian connectedness. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 30–41, 2000