The Radio Number of Gear Graphs

Details The Radio Number of Gear Graphs The Radio Number of Gear Graphs

2008-09-15

arxiv.org/abs/0809.2623v1

Mathematics

Combinatorics

7 pages, 4 figures

Scientific paper

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 $d(u,v)+|c(u)-c(v)|\geq \diam(G) + 1.$ 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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