journal6 ›› 2011, Vol. 32 ›› Issue (6): 5-10.

• Mathematics • Previous Articles     Next Articles

Vertex-Distinguishing Total Coloring of Graph  Pm×P3(n=11+8k) and the Algorithm


  1. (1.School of Information Science and Engineering,Lanzhou City University,Lanzhou 730070,China;2.Institute of Applied Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China)
  • Online:2011-11-25 Published:2012-03-22

Abstract: Let A be a set consisted of all combinations which are made up of four numbers selected from the set {1,2,…,n} discretionarily.By the triangle compositor,the author obtain that for any two adjacent elements C and D in set A,they contain the same three elements.In this paper,using the above idea and n+8k3-n3≡0 (mod 4),it is proved that when n=11+8k(k=0,1,…) and n-14/2+2 <m≤n4/2+2,vertex distinguishing total chromatic number of product Pm×P3 is n.

Key words: product graph, vertex distinguishing toal coloring, vertex distinguishing total chromatic number, triangle sequence

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