The Radio Number of Gear Graphs

2008/09/15 by Christina Fernandez, Fernandez, Christina, América Flores +6 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO #msc:05C78

paper · pdf · doi:10.48550/arxiv.0809.2623

7 pages, 4 figures

arxiv created 2008/09/15 · arxiv updated 2009/12/01

Abstract

Let d(u,v) denote the distance between two distinct vertices of a connected graph G, and \diam(G) be the diameter of G. A radio labeling c of G is an assignment of positive integers to the vertices of G satisfying d(u,v)+|c(u)-c(v)|≥ \diam(G) + 1. The maximum integer in the range of the labeling is its span. The radio number of G, rn(G), is the minimum possible span. The family of gear graphs of order n, G_n, consists of planar graphs with 2n+1 vertices and 3n edges. We prove that the radio number of the n-gear is 4n+2.

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• Cartesian powers of graphs and consecutive radio labelings
• A Dynamic Survey of Graph Labeling

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