The L(2,1)-labeling problem on ditrees

Abstract

An L(2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that f(x)-f(y) greater than or equal to 2 if d(G)(x,y) =1 and f(x)-f(y) greater than or equal to 1 if d(G)(x,y) = 2. The L(2, 1)-labeling problem is to find the smallest number lambda(G) such that there exists a L(2, 1)-labeling function with no label greater than lambda(G). Motivated by the channel assignment problem introduced by Hale, the L(2, 1)-labeling problem has been extensively studied in the past decade. In this paper, we study this concept for digraphs. In particular, results on ditrees are given.