- Internet Math.
- Volume 4, Number 1 (2007), 65-86.
Real Number Labelings for Paths and Cycles
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.
Internet Math., Volume 4, Number 1 (2007), 65-86.
First available in Project Euclid: 27 May 2009
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Griggs, Jerrold R.; Jin, Xiaohua Teresa. Real Number Labelings for Paths and Cycles. Internet Math. 4 (2007), no. 1, 65--86. https://projecteuclid.org/euclid.im/1243430568