图的同构摘要：图论是数学领域中一个非常重要的分支。数学分支中的以下学科如：概率论、矩阵论、数值分析和图论也有着千丝万缕的联系。图论中的图就是我们的研究对象，而在图形中，我们通常用点来替代对象，用点与点之间的线段来代替对象与对象建立的某种必定的关系。作为数学学科和其他学科如计算机学科彼此影响和渗透的纽带，图论是创建和研讨离散数学模型的一个重要工具。自计算机在20世纪50年代后的迅速发展以及大力的推动了图论的发展，使得图论迅速成为数学领域中的佼佼者。77533

目前图论不仅存在于数学学科领域，在计算机学科、电子学科、运筹学科、经济管理学科等领域也有着非常广泛的应用。由于图论本身具有丰富的算法和广泛应用，所以图论问题一直以来在信息类竞赛和数学建模中都占有比较大的比例。图的遍历、最短路径、匹配问题、最小生成树、网络流、图的着色以及图的连通性都是图论中常见的问题。

同构这个词的概念在定义数学对象之间的一类映射是非常重要的，因为它可以揭示出这些对象的属性或者这些对象本身之间的联系。同构是欧式空间或者线性空间这两者之间的一种关系。如果欧式空间和线性空间是同构关系，那么它们就具有了相同的性质，所以对于理解欧式空间或者线性空间来说同构是种“催化剂”。

所谓图的同构个人简单理解就是两个图的结构全部相同，想要迅速并且有精确的判断出两个图是不是同构图在实际的生活应用中是相当重要的，不过对于图的同构这个问题想要彻底解决目前是有一定难度的，因为迄今为止都还没有找到鉴定两个图同构的简易技巧或者算法。当两个图是相对简易而且我们又可以直观的认定是同构图的时候，可以用简单定义来进行判定；当两个图比较复杂的时候，我们可以对图进行旋转、翻转以及变形等手段进行初步判定，然后使用邻接矩阵或者关联度序列的方法对图是否同构进行判定。

毕业论文关键词：图论；同构；图的同构；同构图的判定

The isomorphism of graphs

Abstract: Graph theory is an extraordinary significant branch in mathematics。 The other mathematics branches, such as probability theory, matrix theory and numerical analysis, all have different kinds of connections with graph theory。 The graph in the graph theory is our target of research, but we usually replace objects with points, and replace certain relationship between objects and objects with line segments between points。 As a bond between mathematics and other disciplines, such as computer science, the graph theory is a momentous tool for creating and studying discrete mathematical models。 Since the rapid development of computer in 1950s and the development of the graph theory, the graph theory has rapidly become a leader in the field of mathematics。 

At present the graph theory does not only exist in the field of mathematical disciplines, but also has widely applications in computer science, electronics, operation research, economics and economic management, and so on。 Since the graph theory itself has rich algorithms and extensive applications, the graph theory has occupied a huge scale in the information competitions and mathematical modeling all the time。 Traverse of graphs, shortest path, matching problem, minimum spanning tree, network flow, graphs coloring and connectivity of graphs are common issues in the graph theory。

The concept of isomorphism is extremely important in defining a class mapping between mathematical objects, because it can reveal the properties of these objects or the connections between them。 Isomorphism is a relationship either Euclidean space or linear space。 If the Euclidean space and linear space are isomorphic, then they have the same properties。 So the isomorphism is a “catalyst” for understanding Euclidean space or linear space。