J4 ›› 2011, Vol. 46 ›› Issue (8): 95-103.
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ZHU Hai-yang1, HOU Li-feng1, CHEN Wei1, Lü Xin-zhong2
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Abstract:
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
ZHU Hai-yang1, HOU Li-feng1, CHEN Wei1, Lü Xin-zhong2. The L(p,q)-labeling of planar graphs with girth g(G)≥5[J].J4, 2011, 46(8): 95-103.
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