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2007 Real Number Labelings for Paths and Cycles
Jerrold R. Griggs, Xiaohua Teresa Jin
Internet Math. 4(1): 65-86 (2007).


The problem of radio channel assignments with multiple levels of interference depending on distance can be modelled using graph theory. The authors previously introduced a model of labeling by real numbers. Given a graph $G$, possibly infinite, and real numbers $k_1,k_2\ge0$, an $L(k_1,k_2)$-labeling of $G$ assigns real numbers $f(x)\ge0$ to the vertices $x$, such that the labels of vertices $u$ and $v$ differ by at least $k_i$ if $u$ and $v$ are at distance $i$ apart. We denote by $\lambda(G;k_1,k_2)$ the infimum span over such labelings~$f$. It is enough to determine $\lambda(G;k,1)$ for reals $k\ge0$, which will be a continuous nondecreasing piecewise linear function. Here we present these functions for paths, cycles, and wheels.


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Jerrold R. Griggs. Xiaohua Teresa Jin. "Real Number Labelings for Paths and Cycles." Internet Math. 4 (1) 65 - 86, 2007.


Published: 2007
First available in Project Euclid: 27 May 2009

zbMATH: 1167.05044
MathSciNet: MR2492175

Rights: Copyright © 2007 A K Peters, Ltd.


Vol.4 • No. 1 • 2007
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