d-strong total colorings of cycles when 35<=d<=55
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摘要: 对于图G=(V,E)的一个正常全染色, 用C(v)表示顶点v\in V的颜色以及与 v 关联的边的颜色构成的集合, 称之为点v\in V的色集合. 如果 C(u)\neq C(v), 那么就说u和v被该全染色所区别.一个图 G的 d-强全染色是指使得满足 1\leq d_{G}(u,v)\leq d的任意一对顶点 u 和 v 可区别 的一个正常全染色. 所谓一个图 G 的d-强全色数是指对图 G 进行d-强全染色所需要的颜色的数目的最小值. 文中对当$d\in [35,55]$时圈的 d-强全色数进行 了确定.Abstract: For a proper total coloring of a graph G=(V,E), thepalette C(v) of a vertex v\in V is the set of the colors of the edges incident with v and the color of the vertex itself. If C(u)\neq C(v), then the two vertices u and v of G are said to be distinguished by the total coloring. A d-strong total coloring of G is a proper total coloring that distinguishes all pairs of verticeu and vwith distance 1\leq d_{G}(u,v)\leq d. The d-strong total chromatic number chi^{''}_{d}(G) of Gis the minimum number of colors of a d-strong total coloring ofG. In this paper we determine \chi^{''}_{d}(C_{n}) completely for cycles where d\in [35,55]$ and $d\in \textbf{N
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