For nonnegative integers d1, d2, and L(d1, d2)-labeling of a graph G, is a function f : V(G) → {0, 1, 2, . . .} such that |f(u) − f(v)| ≥ di whenever the distance between u and v is i in G, for i = 1, 2. The L(d1, d2)-number of G, λd1,d2(G) is the smallest k such that there exists an L(d1, d2)-labeling with the largest label k. These labelings have an application to a computer code assignment problem. The task is to assign integer ‘control codes’ to a network of computer stations with distance restrictions, which allow d1 ≤ d2. In this article, we will study the labelings with (d1, d2) ∈ {(0, 1), (1, 1), (1, 2)}.
