A complete [formula omitted] span characterization for small trees

Abstract

An L(2,1) labeling of a graph G is a vertex labeling such that any pair of vertices vi and vj must have labels at least 2 apart if d(vi,vj)=1 and labels at least 1 apart if d(vi,vj)=2. The span of an L(2,1) labeling f on a graph G is the maximum f(u) for all u∈V(G). The L(2,1) span of a graph G is the minimum span of all L(2,1) labelings on G. The L(2,1) labeling on trees has been extensively studied in recent years. In this paper we present a complete characterization of the L(2,1) span of trees up to twenty vertices.