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Issue 6
Dec.  2015
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HUANG Xiao-Jia, CHEN Xiang-恩, WANG Zhi-Wen. d-strong total colorings of cycles when 35Journal of East China Normal University (Natural Sciences), 2015, (6): 30-35.
Citation: HUANG Xiao-Jia, CHEN Xiang-恩, WANG Zhi-Wen. d-strong total colorings of cycles when 35<=d<=55[J]. Journal of East China Normal University (Natural Sciences), 2015, (6): 30-35.

d-strong total colorings of cycles when 35<=d<=55

  • Received Date: 2014-09-09
  • Publish Date: 2015-11-25
  • 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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