若干图的邻点强可区别E-全染色

发布时间：2018-07-26 07:08

【摘要】：设G(V,E)是一个简单图,存在正整数k,如果映射f:E(G)∪V(G)→{1,2,…,k}满足:对(?)uv∈E(G),f(u) ≠ f(v),f(v) ≠ f(uv),f(u) ≠ f(uv).对(?)uv∈E(G),C(u)≠C(v),其中C(u)={f(u)} ∪ {f(v)} ∪ {f(uv)|uv ∈ E(G)]}.则称f是图G的k-邻点强可区别E-全染色,简记为k-E-AVSDTC.称χaste(G) =min{k|G所有k-邻点强可区别E-全染色}为图G的邻点强可区别E-全色数.本文利用色集分配法、反证法、组合分析法、构造函数法,探讨了若干直积图、若干联图和冠图、若干路、圈运算图的邻点强可区别E-全染色问题,并得到了相应图的邻点强可区别E-全色数,最后运用概率方法得到了图的邻点强可区别E-全色数的两个界.论文共分为五个部分:第一部分介绍了本文所涉及的相关概念和已经得到的一些结果.第二部分讨论了笛卡尔直积图、强矢积图、字典积、半强矢积图的邻点强可区别E-全染色,并给出了其相应的色数.第三部分讨论了几类联图和冠图的邻点强可区别E-全染色,并给出了其相应的色数.第四部分讨论了路、圈运算图的邻点强可区别E-全染色,并给出了其相应的色数.第五部分运用概率方法研究了图邻点强可区别E-全色数的两个上界.
[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.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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