网络图在产品配送中的应用

面对多样化的市场需求，企业的销售渠道也变得异常复杂，利用网络图可以简化实际问题，并能形象地描述它。本根据网络知识建立了产品分销模型，探求企业在市场需求固定和随机时的最优收益。最后，章还进行实例验算，并做出相应的结果分析。     

关于带宽极值问题的一些结果

本文研究的问题是确定f(p,B）的值，也就是给定顶点数p和带宽B，求满足最大度不超过B的连通图的最小边数，本文给出了一些f(p,B）的值及相应极图。     

子图识别的层分解方法

子图识别问题(SRP)就是在一个图G中确定并寻找是否存在和另一个图H相同构的子图．本文将引入图的层分解概念，并以此为基础建立识别图的同构子图的算法．该算法的复杂性为O(n(△-1)^k-1)，其中△是图G的度，即G中点的最大度，n，k分别是图G，H的阶．     

关于二部图Km1m2-Hm2的升分解

在文献[2]中作者定义了图的一种新分解-升分解(Ascending subgraph Decomposition简记为ASD)，并提出了一个猜想：任意有正数条边的图都可以升分解．本文主要证明了二部图Km1m2-Hm2(m1≥m2)可以升分解，其中Hm2是至多含m2条边的Km1m2的子图．     

纵横扩张的优化

得到了最小折数纵横扩张的判别准则．针对4-正则图的平面嵌入的纵横扩张的特殊性，给出了它的最小折数纵横扩张判别准则．     

谱半径前六位的n阶单圈图

恰含一个圈的简单连通图称为单圈图。Cn记n个顶点的圈。△（i,j,κ）记C3的三个顶点上分别接出i,j,κ条悬挂边所得的图，其中i≥j≥κ≥0.Sl^n-l记Cl的某一顶点上接出n-l条悬挂边所得到的图。△（n-4 1,0,0)记△（n-4,0,0)的某个悬挂点上接出一条悬挂边所得到的图。本文证明了：若把所有n(n≥12）阶单圈图按其最大特征值从大到小的顺序排列，则排在前六位的依次是S3^n-3，△（n-4,1,0),△（n-4 1,0,0),S4^n-4,△（n-5,2,0),△（n-5,1,1)。     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

The traveling salesman problem in graphs with some excluded minors

Given a graph and a length function defined on its edge-set, the Traveling Salesman Problem can be described as the problem of finding a family of edges (an edge may be chosen several times) which forms a spanning Eulerian subgraph of minimum length. In this paper we characterize those graphs for which the convex hull of all solutions is given by the nonnegativity constraints and the classical cut constraints. This characterization is given in terms of excluded minors. A constructive characterization is also given which uses a small number of basic graphs.     

Multi-Scale Aggregation Graph Neural Networks Based on Feature Similarity for Semi-Supervised Learning

The problem of extracting meaningful data through graph analysis spans a range of different fields, such as social networks, knowledge graphs, citation networks, the World Wide Web, and so on. As increasingly structured data become available, the importance of being able to effectively mine and learn from such data continues to grow. In this paper, we propose the multi-scale aggregation graph neural network based on feature similarity (MAGN), a novel graph neural network defined in the vertex domain. Our model provides a simple and general semi-supervised learning method for graph-structured data, in which only a very small part of the data is labeled as the training set. We first construct a similarity matrix by calculating the similarity of original features between all adjacent node pairs, and then generate a set of feature extractors utilizing the similarity matrix to perform multi-scale feature propagation on graphs. The output of multi-scale feature propagation is finally aggregated by using the mean-pooling operation. Our method aims to improve the model representation ability via multi-scale neighborhood aggregation based on feature similarity. Extensive experimental evaluation on various open benchmarks shows the competitive performance of our method compared to a variety of popular architectures.     

FTRLIM: Distributed Instance Matching Framework for Large-Scale Knowledge Graph Fusion

Instance matching is a key task in knowledge graph fusion, and it is critical to improving the efficiency of instance matching, given the increasing scale of knowledge graphs. Blocking algorithms selecting candidate instance pairs for comparison is one of the effective methods to achieve the goal. In this paper, we propose a novel blocking algorithm named MultiObJ, which constructs indexes for instances based on the Ordered Joint of Multiple Objects’ features to limit the number of candidate instance pairs. Based on MultiObJ, we further propose a distributed framework named Follow-the-Regular-Leader Instance Matching (FTRLIM), which matches instances between large-scale knowledge graphs with approximately linear time complexity. FTRLIM has participated in OAEI 2019 and achieved the best matching quality with significantly efficiency. In this research, we construct three data collections based on a real-world large-scale knowledge graph. Experiment results on the constructed data collections and two real-world datasets indicate that MultiObJ and FTRLIM outperform other state-of-the-art methods.