L(p,q)-labelling of K4-minor free graphs

Authors:
Wang Weifan;Wang Yiqiao
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Venue:
Information Processing Letters
Year:
2006

Citing 7
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Abstract

For positive integers p and q, an L(p,q)-labelling of a graph G is a function @f from the vertex set V(G) to the integer set {0,1,...,k} such that |@f(x)-@f(y)|=p if x and y are adjacent and |@f(x)-@f(y)|=q if x and y are at distance 2. The L(p,q)-labelling number @l(G;p,q) of G is the smallest k such that G has an L(p,q)-labelling with max{@f(v)|v@?V(G)}=k. In this paper we prove that, if p+q=3 and G is a K"4-minor free graph with maximum degree @D, then @l(G;p,q)==4.