Graph distance‐dependent labeling related to code assignment in computer networks

Xiaohua Teresa Jin and Roger K. Yeh

Naval Research Logistics (NRL), 2005, vol. 52, issue 2, 159-164

Abstract: 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, λ d 1,d 2(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, 2005

Date: 2005
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