【摘要】：設(shè)G(V,E)是一個(gè)簡單圖,存在正整數(shù)k,如果映射f:E(G)∪V(G)→{1,2,…,k}滿足:對(?)uv∈E(G),f(u) ≠ f(v),f(v) ≠ f(uv),f(u) ≠ f(uv).對(?)uv∈E(G),C(u)≠C(v),其中C(u)={f(u)} ∪ {f(v)} ∪ {f(uv)|uv ∈ E(G)]}.則稱f是圖G的k-鄰點(diǎn)強(qiáng)可區(qū)別E-全染色,簡記為k-E-AVSDTC.稱χaste(G) =min{k|G所有k-鄰點(diǎn)強(qiáng)可區(qū)別E-全染色}為圖G的鄰點(diǎn)強(qiáng)可區(qū)別E-全色數(shù).本文利用色集分配法、反證法、組合分析法、構(gòu)造函數(shù)法,探討了若干直積圖、若干聯(lián)圖和冠圖、若干路、圈運(yùn)算圖的鄰點(diǎn)強(qiáng)可區(qū)別E-全染色問題,并得到了相應(yīng)圖的鄰點(diǎn)強(qiáng)可區(qū)別E-全色數(shù),最后運(yùn)用概率方法得到了圖的鄰點(diǎn)強(qiáng)可區(qū)別E-全色數(shù)的兩個(gè)界.論文共分為五個(gè)部分:第一部分介紹了本文所涉及的相關(guān)概念和已經(jīng)得到的一些結(jié)果.第二部分討論了笛卡爾直積圖、強(qiáng)矢積圖、字典積、半強(qiáng)矢積圖的鄰點(diǎn)強(qiáng)可區(qū)別E-全染色,并給出了其相應(yīng)的色數(shù).第三部分討論了幾類聯(lián)圖和冠圖的鄰點(diǎn)強(qiáng)可區(qū)別E-全染色,并給出了其相應(yīng)的色數(shù).第四部分討論了路、圈運(yùn)算圖的鄰點(diǎn)強(qiáng)可區(qū)別E-全染色,并給出了其相應(yīng)的色數(shù).第五部分運(yùn)用概率方法研究了圖鄰點(diǎn)強(qiáng)可區(qū)別E-全色數(shù)的兩個(gè)上界.
[Abstract]:Let G (V, E) be a simple graph, there is a positive integer k, if mapping f:E (G) V V (G) to {1,2,... Diagram drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing diagram drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing diagram drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing diagram drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing diagram drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing diagram drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing drawing strong adjacent point In this paper, we use the color set allocation method, the inverse method, the combinatorial analysis method and the constructor method, to discuss some direct product graphs, some joint graph Wacom graphs, some road and ring operation graphs with strong differentiable E- total coloring problems, and get the adjacent strong region E- total color number of the corresponding graphs. Finally, the neighbor points of the graph are obtained by the probability method. The two bounds of the strongly distinguishable E- panchromatic number are divided into five parts. The first part introduces the related concepts and some results that have been obtained in this paper. The second part discusses the Descartes direct product, strong vector product, dictionary product, and semi strong vector product with strong distinguishable E- total coloring, and gives its corresponding chromatic number and third parts. This paper discusses the neighborhood strongly distinguishable E- total coloring of several types of graph Wacom graphs, and gives its corresponding color number. The fourth part discusses the adjacent point strongly distinguishable E- full coloring of the road and loop operation graph, and gives its corresponding chromatic number. The fifth part studies the two upper bounds of the strongly distinguishable E- total color of the graph adjacent to the graph.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5

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