Graph Distance-Dependent Labeling Related to Code Assignment in Computer Networks

For nonnegative integers d1, d2, and L(d1, d2)-labeling of a graph G, is a function f : V(G) 3 {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, d1,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)}. © 2004 Wiley Periodicals, Inc. Naval Research Logistics 51: 000–000, 2004.