J4 ›› 2011, Vol. 46 ›› Issue (4): 4-8.

• Articles • Previous Articles     Next Articles

Adjacent-vertex-distinguishing total coloring of planar bipartite graphs

LI Ze-peng1, WANG Zhi-wen2, CHEN Xiang-en1*   

  1. 1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, Ningxia, China
  • Received:2009-09-28 Published:2011-04-21

Abstract:

A proper total coloring of G is an adjacent vertex distinguishing total coloring if for any two adjacent vertices, the sets of colors appearing on the vertex and incident edges are different. The smallest number of color of which such a coloring of G exists is called the adjacent vertex distinguishing total chromatic number, and is denoted by χat(G). It is proved that χat (G)≤Δ(G)+2 for any planar bipartite graph G with maximum degree Δ(G) at least 11 and grith at least 4.

Key words:  graphs; planar bipartite graphs; adjacent-vertex-distinguishing total coloring; adjacent-vertex-distinguishing total chromatic number

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