本文選題：菲利茨特標號　切入點：優(yōu)美標號　出處：《西北師范大學》2015年碩士論文　論文類型：學位論文

【摘要】：圖的標號研究起源于1966年Rosa[1]提出的著名優(yōu)美樹猜想“每一棵樹都是優(yōu)美樹”.圖的標號是圖的頂點集到整數(shù)集的映射,而根據(jù)邊標號的不同要求產(chǎn)生了各類圖標號.關(guān)于優(yōu)美樹猜想已經(jīng)有了很多結(jié)果,但是眾所周知這一猜想一直沒有被徹底的解決.Sin-Min Lee等人于1991年提出了猜想“每一棵樹都是菲利茨特樹”.該猜想與優(yōu)美樹猜想具有同等的理論價值,而且具有相同的難度,都是NP-hard問題.對于數(shù)學猜想的進攻,導致圖的標號迅速發(fā)展成為當今圖論學科中十分活躍的分支,它在編碼理論、通訊網(wǎng)絡(luò)、物流等方面均有著重要應(yīng)用.本文首先研究了集有序菲利茨特標號與集有序優(yōu)美標號之間的等價關(guān)系,以及利用多個較小的樹構(gòu)造的較大樹的菲利茨特性質(zhì).其次,文章研究了具有廣泛意義的太陽圖的菲利茨特標號.最后,介紹了一種新的標號—奇優(yōu)雅標號,并給出了一些特殊廣義太陽圖的奇優(yōu)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.
【學位授予單位】：西北師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O157.5

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本文編號：1573095