论图的菲利茨特标号

发布时间：2018-03-06 03:15

本文选题：菲利茨特标号　切入点：优美标号　出处：《西北师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：图的标号研究起源于1966年Rosa[1]提出的著名优美树猜想“每一棵树都是优美树”.图的标号是图的顶点集到整数集的映射,而根据边标号的不同要求产生了各类图标号.关于优美树猜想已经有了很多结果,但是众所周知这一猜想一直没有被彻底的解决.Sin-Min Lee等人于1991年提出了猜想“每一棵树都是菲利茨特树”.该猜想与优美树猜想具有同等的理论价值,而且具有相同的难度,都是NP-hard问题.对于数学猜想的进攻,导致图的标号迅速发展成为当今图论学科中十分活跃的分支,它在编码理论、通讯网络、物流等方面均有着重要应用.本文首先研究了集有序菲利茨特标号与集有序优美标号之间的等价关系,以及利用多个较小的树构造的较大树的菲利茨特性质.其次,文章研究了具有广泛意义的太阳图的菲利茨特标号.最后,介绍了一种新的标号—奇优雅标号,并给出了一些特殊广义太阳图的奇优雅性.
[Abstract]:The labeling of graphs originates from the famous graceful tree conjecture "every tree is a graceful tree" put forward by Rosa in 1966. The label of a graph is the mapping of the vertex set of a graph to the set of integers. According to the different requirements of edge labeling, various icon numbers have been produced. There have been many results on the graceful tree conjecture. But it is well known that this conjecture has not been completely solved by Sin-Min Lee et al. In 1991, she put forward the conjecture that "every tree is a Phillips tree". This conjecture has the same theoretical value as the graceful tree conjecture and has the same difficulty. The attack of mathematical conjecture has led to the rapid development of graph labeling into a very active branch of graph theory, which is used in coding theory and communication networks. In this paper, we first study the equivalent relationship between the set ordered Fritt label and the set ordered graceful label, as well as the Fritz property of the larger tree constructed from several smaller trees. In this paper, we study the Fritzt labeling of solar graphs with wide meaning. Finally, we introduce a new kind of label-odd elegant labeling, and give some special generalized solar graphs with odd elegance.
【学位授予单位】：西北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

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