本文選題：圖 + 聯(lián)樹��； 參考：《北京交通大學(xué)》2015年碩士論文

【摘要】：本文主要研究了一般田圖的虧格分布及一些梯圖虧格分布的單峰性。 這里考慮連通無向圖在曲面上的可定向的胞腔嵌入,這里的曲面指的是無邊緣的2-維緊流形。自從1987年圖的虧格分布提出以來,此問題即引起學(xué)者們的關(guān)注。研究的圖類從閉梯、莫比烏斯梯、Ringel梯、圓體及鵝卵石路等幾類特殊圖類,擴(kuò)展到一般梯圖、3-正則圖及4-正則圖等較為復(fù)雜的圖類。用來求圖的嵌入的虧格分布的方法主要有組合的方法、Jackson公式、矩陣法、基于聯(lián)樹的曲面生成法和曲面分類法及分布分解法。 本文在劉彥佩老師提出的聯(lián)樹法的基礎(chǔ)上,通過運(yùn)用曲面分類法,分類一類新圖類的可定向嵌入曲面,計算一些曲面集的虧格分布,把一般田圖的虧格分布轉(zhuǎn)化為這些曲面集的線性組合,從而求出這類圖的可定向嵌入的虧格分布。推廣了Gross等關(guān)于P3□Pn虧格分布的計算,并把他們的結(jié)果簡單地導(dǎo)出。最后,給出一些梯圖的虧格分布的單峰性。 第一章對圖的虧格分布、在可定向曲面上的嵌入的相關(guān)概念及研究做簡要介紹。 第二章首先求出一些曲面集的虧格分布的遞推表達(dá)式,在聯(lián)樹的基礎(chǔ)上,運(yùn)用曲面分類法把一般田圖的虧格分布轉(zhuǎn)化為這些曲面集的線性組合。對P3□Pn,用聯(lián)樹法及分布分解法,求出其虧格分布的遞推表達(dá)式,然后運(yùn)用計算機(jī)編程計算出其虧格分布。另外,得到了幾類梯圖的虧格分布。 第三章本章主要研究了多項式序列的單峰性和對數(shù)凹之間的相關(guān)關(guān)系。第二部分,得到了關(guān)于有限個單峰序列的線性組合是否單峰的準(zhǔn)則；第三部分,回顧了梯圖曲面集的虧格分布是單峰的或?qū)?shù)凹的,并給出梯圖曲面集虧格分布的峰點公式；第四部分,證明了一些梯圖的虧格分布的單峰性,并給出這些梯圖虧格分布的峰點公式。
[Abstract]:In this paper, we mainly study the genus distribution of general field graphs and the unimodal properties of some ladder graph genus distributions.In this paper, we consider the orientable cell embedding of connected undirected graphs on surfaces, where the surfaces refer to 2-dimensional compact manifolds without edges.Since the genus distribution of graphs was put forward in 1987, this problem has attracted the attention of scholars.The graphs are extended from the closed ladder, Mobius ladder Ringel ladder, circular body and cobblestone path to the general ladder 3-regular graphs and 4-regular graphs.The methods used to find the embedded genus distribution of graphs include the combination of Jackson formula, the matrix method, the surface generation method based on the combined tree, the surface classification method and the distribution decomposition method.In this paper, on the basis of the combined tree method proposed by Liu Yanpei, the genus distribution of some surface sets is calculated by using the surface classification method to classify the orientable embedded surfaces of a new class of graphs.The genus distribution of a general field graph is transformed into a linear combination of these surface sets, and the directed embeddable genus distribution of this kind of graph is obtained.In this paper, we generalize the calculation of P3-Pn genus distribution by Gross et al, and simply derive their results.Finally, the singularity of genus distribution of some ladder graphs is given.The first chapter briefly introduces the genus distribution of graphs, the related concepts and research of embedding on orientable surfaces.In the second chapter, the recursion expressions of genus distribution of some surface sets are obtained. On the basis of the combined tree, the genus distribution of the general field graph is transformed into the linear combination of these surface sets by using the surface classification method.For P3-Pn, the recursive expression of genus distribution is obtained by using the method of combined tree and the method of distribution decomposition, and then the genus distribution is calculated by computer programming.In addition, the genus distributions of several kinds of ladder graphs are obtained.In chapter 3, we study the correlation between the unimodal property and logarithmic concave of polynomial sequences.In the second part, we obtain the criterion of whether the linear combination of finite unimodal sequences is unimodal, in the third part, we review that the genus distribution of ladder graph surface set is unimodal or logarithmic concave, and give the peak point formula of the genus distribution of ladder graph surface set.In the fourth part, we prove the unimodal property of the genus distribution of some ladder graphs, and give the peak point formula of the genus distribution of these ladder graphs.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 李立峰,劉彥佩;一類三正則圖的嵌入虧格分布[J];北京交通大學(xué)學(xué)報;2004年06期

2 萬良霞;劉彥佩;;一類新圖類的可定向嵌入的虧格分布[J];北京交通大學(xué)學(xué)報;2005年06期

3 李德明;Genus Distribution for Circular Ladders[J];Northeastern Mathematical Journal;2000年02期

4 李德明;Genus Distributions of M(o|¨)bius Ladders[J];Northeastern Mathematical Journal;2005年01期

5 ;The genus distributions for a certain type of permutation graphs in orientable surfaces[J];Science in China(Series A:Mathematics);2007年12期

6 趙喜梅;劉彥佩;;類樹圖虧格分布的單峰性[J];山西大學(xué)學(xué)報(自然科學(xué)版);2006年03期

7 李興闊;郝榮霞;周建梅;;燈籠圖的可定向嵌入虧格分布[J];數(shù)學(xué)進(jìn)展;2010年02期

8 黃元秋,劉彥佩;圖的最大虧格與2-因子[J];數(shù)學(xué)年刊A輯(中文版);1997年05期

9 趙喜梅;劉彥佩;;類圈圖的虧格分布[J];數(shù)學(xué)物理學(xué)報;2008年04期

10 楊艷;劉彥佩;;兩類四正則圖的完全虧格分布[J];數(shù)學(xué)學(xué)報;2007年05期

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本文編號：1750767