Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 2 (2016), 317-332.

Radio number for fourth power paths

Min-Lin Lo and Linda Victoria Alegria

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Abstract

Let G be a connected graph. For any two vertices u and v, let d(u,v) denote the distance between u and v in G. The maximum distance between any pair of vertices of G is called the diameter of G and denoted by diam(G). A radio labeling (or multilevel distance labeling) of G is a function f that assigns to each vertex a label from the set {0,1,2,} such that the following holds for any vertices u and v: |f(u) f(v)| diam(G) d(u,v) + 1. The span of f is defined as maxu,vV (G){|f(u) f(v)|}. The radio number of G is the minimum span over all radio labelings of G. The fourth power of G is a graph constructed from G by adding edges between vertices of distance four or less apart in G. In this paper, we completely determine the radio number for the fourth power of any path, except when its order is congruent to 1(mod8).

Article information

Source
Involve, Volume 9, Number 2 (2016), 317-332.

Dates
Received: 24 November 2014
Revised: 12 April 2015
Accepted: 12 April 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511371003

Digital Object Identifier
doi:10.2140/involve.2016.9.317

Mathematical Reviews number (MathSciNet)
MR3470734

Zentralblatt MATH identifier
1333.05266

Subjects
Primary: 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

Keywords
channel assignment problem multilevel distance labeling radio number radio labeling

Citation

Lo, Min-Lin; Alegria, Linda Victoria. Radio number for fourth power paths. Involve 9 (2016), no. 2, 317--332. doi:10.2140/involve.2016.9.317. https://projecteuclid.org/euclid.involve/1511371003


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