图上的概率分布及位置方向信息的表征方法  

Probability distributions on graphs and characterization methods for place direction information

作　　者：张孝伍[1] ZHANG Xiao-wu(School of Science,Qingdao University of Technology,Qingdao 266520,China)

机构地区：[1]青岛理工大学理学院,青岛266520

出　　处：《青岛理工大学学报》2019年第1期113-121,共9页Journal of Qingdao University of Technology

摘　　要：已经有多种不变量来分辨不同构的图,但这些不变量都是不完全的.运用地图的同构算法、对偶性、概率论和神经信息学的感受野理论,研究了图的结构信息描述和图的同构问题.对于给定图G=(V,E)、超图H=H(V,E)和地图M=(V,E,F),由节点集的邻域结构,给出了G、H和M上的节点集V、边集E和面集F的结构概率分布.借助于每个节点的距离邻域结构和排序信息,得到了节点、边和面在地图上位置方向信息的表征方法,并且给出了地图的同构完全不变量.There have been multifarious invariants to distinguish the isomorphism of graphs,but these invariants are incomplete.Using the isomorphic algorithm of graphs,duality,probability theory and receptive field theory of neuroinformatics,the structural information description of graphs and the isomorphism problem of graphs are studied.For a given graph G=(V,E),hypergraph H=H(V,E),and the map M=(V,E,F),from the neighborhood structure of the node set,the structure probability distributions for node set V and edge sets E and face set F are given.The characterization methods for place direction information are obtained by the aid of distance neighborhood structures and sorting information of each node,and the isomorphic invariants of maps are given.

关 键 词：表征方法 概率分布 位置方向信息 地图 同构不变量 

分 类 号：O157.5[理学—数学] B845[理学—基础数学]