L(p,q)-Labelling of Outerplanar Graphs

For integers p,q,n0, a labelling of a graphφ:V(G)→｛0,1,2,…,n｝is called an L(p,q)-labelling if it satisfies:|φ(u)-φ(v)|≥p whenever and dist_G()(u,v)=1;|φ(u)-φ(v)|≥qwhenever dist_G()(u,v)=2. The (p,q)-span of a graph_G, denoted by λ(G;p,q), is the minimum n for which an L(p,q)-labelling exists. In this article we proved that: Let G be an outerplanar graph with maximal degree Δ, then. λ(G;p,q)≤qΔ+4p+2q-4.