J4 ›› 2011, Vol. 46 ›› Issue (8): 95-103.

• Articles • Previous Articles     Next Articles

The L(p,q)-labeling of planar graphs with girth g(G)≥5

ZHU Hai-yang1, HOU Li-feng1, CHEN Wei1, Lü Xin-zhong2   

  1. 1. Department of Logistics Command, Xuzhou Air Force College, Xuzhou 221000, Jiangsu, China;
    2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
  • Received:2010-05-18 Online:2011-08-20 Published:2011-09-08


Let p and q be two positive integers with p≥q, and let λp,q(G) be the L(p,q)-labeling number of a planar graph G. It is proved that λp,q(G)≤(2q-1)Δ(G)+6p+10q-8 if  G is a planar graphs with girth g(G)≥5, which implies Wegner’s conjecture holds for a planar graph G with girth g(G)≥5 and Δ(G)≥16.

Key words:  planar graph;girth; L(p,q)-labeling; L(p,q)-labeling number

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