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

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  • Xiaohua Teresa Jin
  • Roger K. Yeh

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

Suggested Citation

  • Xiaohua Teresa Jin & Roger K. Yeh, 2005. "Graph distance‐dependent labeling related to code assignment in computer networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(2), pages 159-164, March.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:2:p:159-164
    DOI: 10.1002/nav.20041
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    Cited by:

    1. Jerrold R. Griggs & Xiaohua Teresa Jin, 2007. "Recent progress in mathematics and engineering on optimal graph labellings with distance conditions," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 249-257, October.
    2. Qiong Wu & Wai Chee Shiu & Pak Kiu Sun, 2014. "Circular L(j,k)-labeling number of direct product of path and cycle," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 355-368, February.

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