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  本文選題：正常邊染色 + 正常全染色��； 參考：《中國礦業(yè)大學》2017年碩士論文

【摘要】：對于圖(7)EVG,(8),給定一個正整數(shù)k,一個正常k邊染色是一個映射c?{.....2,1:kE},對于任意兩條相互關聯(lián)的邊?(7)GE(8)21e,e,有(7)(8)(7)(8)21ecec1。一個正常k全染色是一個映射V?{.....2,1:kEc}U,使得每一對相鄰的點和相鄰的邊以及相關聯(lián)的點和邊所對應的值不一樣。設c是G的一個正常邊染色,對(7)GV(8)中任意一點v,令?(7)vc(8)代表與v相關聯(lián)的邊的顏色之和,如果對(7)GE(8)中的每條邊uv,有(7)(8)?1?(7)vcuc(8),那么這樣一個正常邊染色叫做鄰和可區(qū)別邊染色,滿足這種染色的最小k值叫做鄰和可區(qū)別邊色數(shù),用(7)G(8)?c￠來表示。類似地對于圖(7)EVG,(8)的正常全染色,對于(7)GV(8)中任意一點v,令?(7)vs(8)代表與v相關聯(lián)的邊的顏色與點v的顏色之和。如果對(7)GE(8)中的每條邊uv,有(7)(8)?1?(7)vsus(8),那么這樣一個正常全染色叫做鄰和可區(qū)別全染色。滿足這種染色的最小k值叫做鄰和可區(qū)別全色數(shù),用(7)G(8)?c￠來表示。本文主要證明了兩個定理,第一個定理,對于不含孤立邊的簡單圖G,如果(7)Gmad(8)(27)310,那么￠(7)(8)kG￡?c,其中,k{(10)(35)(28)14,2max}。第二個定理,對于平面圖G,如果(7)G(8)3(35)5且(7)Gg(8)35,那么￠(7)(8)(7)(8)(10)(35)￡3?cGG。本文主要內(nèi)容具體分為四章展開:第一章,介紹研究領域的相關背景及本文用到的基本概念和研究現(xiàn)狀。第二章,利用歐拉公式及權轉(zhuǎn)移規(guī)方法證明了第一個定理。第三章,利用權轉(zhuǎn)移法規(guī)則構(gòu)造反例證明了第二個定理。第四章,對本文的結(jié)果進行了簡單的總結(jié)并作了進一步的展望。
[Abstract]:Given a positive integer k, a normal k-edge coloring is a mapping? {....2n 1: KE}, and for any two interrelated edges, there is a positive integer k, a normal k-edge coloring is a map c {.....2n 1: KE}, and for any two interrelated edges, there is a positive integer k, a normal k-edge coloring is a map c {.......A normal k-total coloring is a mapping V {{.....2n 1: KEC} U, such that each pair of adjacent points and adjacent edges and the associated points and edges correspond to different values.Let c be a normal edge coloring of G, so that any point vin 7 / GV) so that the sum of the colors of the edges associated with v is represented, if for each edge UV in 7 / G / 8) there is a 7 / 7 / 7 / v cuc8s, then such a normal edge dyeing is called adjacent and distinguishable edge dyeing.The minimum k value satisfying this kind of coloring is called the adjacent and differentiable edge chromatic number, which is expressed in the form of 7 ~ (7) G ~ (+) ~ (8) C.Similarly, for the normal total coloring of fig. 7 / EVGG), for any point of v8), such a v8) represents the sum of the color of the edge associated with v and the color of the dot v.If for each edge UV, there is a normal total dyeing called adjacent and distinguishable total dyeing.The minimum k value satisfying this kind of coloring is called adjacent and distinguishable total chromatic number, which is expressed in terms of 7 ~ (7) G ~ (+) ~ ((8)) C.In this paper, we mainly prove two theorems. The first theorem is that for a simple graph G with no isolated edges, if the graph G is 7 / 7 / G / 8 / 27 / 310, then 7 / 7 / 8 / 8kG / c, in which k {10 / 10 / 35 / 28 / 14 / 2max}.The second theorem is that for the planar graph G, if there are 7g ~ (8) ~ 3 ~ ~ ~ (5) and ~ ~ (7) G ~ (g) ~ (8) ~ ~ ~ (35), then there is no _ _ _The main contents of this paper are divided into four chapters: the first chapter introduces the relevant background of the research field, the basic concepts used in this paper and the current research situation.In chapter 2, the first theorem is proved by using Euler formula and weight transfer gauge method.In chapter 3, the second theorem is proved by using the rule of weight transfer to construct counterexample.In the fourth chapter, the results of this paper are summarized and further prospects are given.
【學位授予單位】：中國礦業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O157.5

【參考文獻】

相關期刊論文 前2條

1 DING LaiHao;WANG GuangHui;YAN GuiYing;;Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz[J];Science China(Mathematics);2014年09期

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本文編號：1751251