极大3限制边连通二部图的充分条件

设G=(V,E)是一个连通图.称一个边集合S■E是一个k限制边割,如果G-S的每个连通分支至少有k个顶点.称G的所有k限制边割中所含边数最少的边割的基数为G的k限制边连通度,记为λ_k(G).定义ξ_k(G)=min{[X,■]:|X|=k,G[X]连通,■=V(G)\X}.称图G是极大k限制边连通的,如果λ_k(G)=ξ_k(G).本文给出了围长为g>6的极大3限制边连通二部图的充分条件.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

基于图像的二维剪纸自动生成方法

中国剪纸的设计极具挑战性, 要求画面简洁、直观, 还需要表达特定的文化内涵, 且整张剪纸须整体连通。提出了一种基于图像的二维剪纸自动生成方法, 能够将任意数码照片自动转化为剪纸图形。首先，利用图像分割方法建立区域连接图; 接着, 基于该连接图对颜色、边界对比度和区域连通性进行数学建模, 并获得优化目标函数; 最后, 通过模拟退火算法求解目标方程, 自动生成保持图像内容的剪纸图形。还开发了连通性后处理和区域指定等用户交互工具, 允许用户在自动生成的剪纸图形中方便地加入个人设计。实验表明, 所生成的剪纸图形画面简洁、整体连通。 本方法在降低剪纸设计难度的同时还可满足个性化的设计需求, 有助于传播和传承我国的民间剪纸艺术。     

On molecular topological properties of hex‐derived networks

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure–activity relationship/quantitative structure–property relationship study, physico‐chemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study hex‐derived networks HDN1(n) and HDN2(n), which are generated by hexagonal network of dimension n and derive analytical closed results of general Randić index R_α(G) for different values of α, for these networks of dimension n. We also compute the general first Zagreb, ABC, GA, ABC₄, and GA₅ indices for these hex‐derived networks for the first time and give closed formulae of these degree‐based indices for hex‐derived networks. Copyright © 2016 John Wiley & Sons, Ltd.     

On the Minimum Number of Spanning Trees in k‐Edge‐Connected Graphs

We show that a k‐edge‐connected graph on n vertices has at least spanning trees. This bound is tight if k is even and the extremal graph is the n‐cycle with edge multiplicities . For k odd, however, there is a lower bound , where . Specifically, and . Not surprisingly, c₃ is smaller than the corresponding number for 4‐edge‐connected graphs. Examples show that . However, we have no examples of 5‐edge‐connected graphs with fewer spanning trees than the n‐cycle with all edge multiplicities (except one) equal to 3, which is almost 6‐regular. We have no examples of 5‐regular 5‐edge‐connected graphs with fewer than spanning trees, which is more than the corresponding number for 6‐regular 6‐edge‐connected graphs. The analogous surprising phenomenon occurs for each higher odd edge connectivity and regularity.     

甲氧基多溴联苯醚色谱相对保留时间的QSRR研究

基于有机化合物定量结构与色谱相对保留时间的关系,对26个甲氧基多溴联苯醚化合物进行了B3LYP/6-31G*水平上的结构优化,并在优化结构基础上进行了分子连接性指数和量子化学结构参数的提取。应用SPSS统计软件对甲氧基多溴联苯醚化合物的色谱相对保留时间与分子连接性指数进行了多元线性回归(MLR)。结果表明,三阶类分子连接性指数可以很好地表达甲氧基多溴联苯醚化合物色谱相对保留时间与结构描述符之间的定量关系。用外部测试集的方法对模型预测能力进行了验证,结果表明:所建立的QSRR模型具有较强的稳健性和预测能力。     

地圈动力学的THMCB多元关联过程及其分析

地圈中广泛发育的动力学过程属于多元关联过程,它们是在岩土圈与水圈、大气圈、生物圈相互作用中进行的。它们的活动可以概括为热力学、流体力学、固体力学、化学和生物学等基本物质运动的作用及系统的演化。由于它们之间有着互动影响和制约,以及由此引发的能量的转换和参数的变异,因而密切相关。本文建议确立THMCB多元关联过程的概念,开展多元关联过程的研究和分析,以期对地圈动力学过程进行系统有效的综合评价和预测。     

On edge connectivity and parity factor

By Petersen's Theorem, a bridgeless cubic graph has a 2-factor. Fleischner(Discrete Math.,101, 33–37(1992)) has extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has an even factor without isolated vertices. Let me 0 be even and mo 0 be odd. In this paper, we prove that every m e-edge-connected graph with minimum degree at least me + 1 contains an even factor with minimum degree at least m e and every(m o + 1)-edge-connected graph contains an odd factor with minimum degree at least m o, which further extends Fleischner's result. Moreover, we show that our results are best possible.