J4 ›› 2011, Vol. 46 ›› Issue (6): 53-56.

• Articles • Previous Articles     Next Articles

A bound of the vertex-distinguishing total chromatic number of graphs

QIANG Hui-ying   

  1. College of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2010-05-17 Online:2011-06-16 Published:2011-12-19


A proper total coloring of the graph G is called vertex-distinguishing total coloring, if any two vertices have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it. On the base of the bound of vertex-distinguishing total chromatic number( χvt ( G)≤|V(G)|+2). The new upper bound of vertex-distinguishing total chromatic number is obtained by way of probability.

Key words:   vertex-distinguishing total coloring; vertex distinguishing total chromatic number;  the Lovász local lemma

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