Computer Engineering and Applications ›› 2012, Vol. 48 ›› Issue (25): 39-41.

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Adjacent vertex-distinguishing I-total chromatic number of some  kinds of  k-multi-Mycielski graph

TIAN Jingjing   

  1. Department of Mathematics, Shaanxi University of Technology, Hanzhong, Shaanxi 723000, China
  • Online:2012-09-01 Published:2012-08-30

若干多重Mycielski图的邻点可区别I-全色数

田京京   

  1. 陕西理工学院 数学系,陕西 汉中 723000

Abstract: According to the properties of the k-multi-Mycielski graph[Mn(Sm)] and [Mn(Cm)],[Mn(Pm)], the adjacent vertex-distinguishing  I-total coloring of some kinds of k-multi-Mycielski graph[Mn(Sm)] and [Mn(Cm)],[Mn(Pm)] have been discussed. The adjacent vertex distinguishing I-total chromatic  number of [Mn(Sm)] and [Mn(Cm)],[Mn(Pm)] has been obtained. And the coloring method of the k-multi-Mycielski graph [Mn(Sm)] and [Mn(Cm)],[Mn(Pm)] has been  given.

Key words: graph, star, path, circle, k-multi-Mycielski graph, adjacent vertex distinguishing I-total coloring, adjacent vertex distinguishing I-total chromatic number

摘要: 根据路和星、圈的多重Mycielski图的结构性质,用穷染递推的方法,讨论了图[Mn(Cm)]和[Mn(Pm)],以及[Mn(Sm)]的邻点可区别I-全染色,得到了图[Mn(Sm)]和[Mn(Pm)]的邻点可区别I-全色数等于它们的最大度,图[Mn(Cm)]的邻点可区别I-全色数在m=4,5时等于它的最大度加1,其余情况等于它的最大度,即分别给出图[Mn(Sm)]和[Mn(Cm)、][Mn(Pm)]一种染色方案。

关键词: 图, 星, 路, 圈, 多重Mycielski图, 邻点可区别I-全染色, 邻点可区别I-全色数