数学归纳法在图论中的应用研究——以图染色算法和图同构问题为例  

The Application of Mathematical Induction in Graph Theory——Concerning Graph Coloring Algorithm and Graph Isomorphism Problem

作　　者：管悦 Guan Yue(Chongqing Yitong College,Chongqing 401520,China)

机构地区：[1]重庆移通学院,重庆401520

出　　处：《黑河学院学报》2024年第12期181-184,共4页Journal of Heihe University

摘　　要：图论是数学中的一个重要分支,与组合数学、控制论、运筹学等有着紧密联系。在众多研究方法和技术手段当中,数学归纳法因其强大的推导功能和分析能力被广泛应用于图论中。数学归纳法在图论中的应用广泛,图论的基本内容涵盖了图的各种要素,其图同构问题涉及图染色算法及几类相关问题(包括最小顶点度为1的三圈图、最少边数的完全图);解决问题的方法有两种,即递归与循环法。数学归纳法是解决图论问题的有力工具,将其合理运用到图论中能够有效地提高解题效率,减少计算时间,提升计算精度,使图论领域获得新突破。Graph theory’s an important branch of mathematics,is closely related to combinatorics,control theory,operations research,and others.Among numerous research methods and technical means,mathematical induction is widely used in graph theory due to its powerful deduction and analysis capabilities.The mathematical induction is widely applied in graph theory as well.The basic content of graph theory involves graph staining algorithm and several related problems(including three-cycle graph with minimum vertex degree of 1 and complete graph with minimum number of edges),which can be solved with two diff erent solutions,namely recursion and loop method.It can be said that mathematical induction is a powerful tool for solving graph theory problems,and that graph theory can be reasonably applied to eff ectively improve problem-solving effi ciency,to reduce computation time,improve computational accuracy,and to make new breakthroughs in the field of graph theory.

关 键 词：图论 数学归纳法 图同构 图染色算法 

分 类 号：O1-0[理学—数学]