几类图的Smarandachely邻点V-全染色

发布时间：2018-05-16 09:28

本文选题：冠图 + Smarandachely邻点V-全染色　；参考：《兰州交通大学》2017年硕士论文

【摘要】：针对图的Smarandachely邻点V-全染色问题,此文用结构分析的方法和构造法研究了图论中常见的部分简单图(子图)和图运算后的图(母图)的Smarandachely邻点V-全染色,得到了它们的色数。并进一步探讨了子图和母图在染色法则下,其色数之间的关系,且找到了一系列反例(子图的色数反而比母图的色数大)。文章共分为四个章节:第一章介绍了有关基础理论;第二章研究了(路、圈、星、扇、轮)构成的冠图的Smarandachely邻点V-全染色,并得到了其色数,从而验证了 Smarandachely邻点V-全染色猜想;第三章研究了三种积图(直积图、笛卡尔积图及半强矢积图)的Smarandachely邻点V-全染色,并得到了其色数;第四章研究了子图和母图在染色法则下其色数之间的关系。
[Abstract]:Aiming at the problem of Smarandachely adjacent vertex V-total coloring of graphs, this paper studies some simple graphs (subgraphs) and Smarandachely adjacent vertex-total coloring of graphs (generating graphs), which are common in graph theory by means of structural analysis and construction, and obtains their chromatic numbers. Furthermore, the relationship between the chromatic number of subgraphs and parent graphs under the coloring rule is discussed, and a series of counterexample (the chromatic number of subgraphs is larger than the chromatic number of parent graphs) is found. This paper is divided into four chapters: the first chapter introduces the basic theory, the second chapter studies the Smarandachely adjacent vertex V-total coloring of the crown graph (path, circle, star, fan, wheel), and obtains its chromatic number. In chapter 3, we study the Smarandachely adjacent vertex V-total coloring of three kinds of product graphs (direct product graph, Cartesian product graph and semi-strong product graph), and obtain their chromatic number. In chapter 4, we study the relationship between the chromatic number of subgraphs and parent graphs under the rule of coloring.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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