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Multilevel Distance Labelings for Paths and Cycles.
- Source :
-
SIAM Journal on Discrete Mathematics . 2005, Vol. 19 Issue 3, p610. 12p. - Publication Year :
- 2005
-
Abstract
- For a graph $G$, let $\diam(G)$ denote the diameter of $G$. For any two vertices $u$ and $v$ in $G$, let $d(u, v)$ denote the distance between $u$ and $v$. A multilevel distance labeling (or distance labeling) for $G$ is a function $f$ that assigns to each vertex of $G$ a nonnegative integer such that for any vertices $u$ and $v$, $|f(u)-f(v)| \geq \diam(G) - d_G(u, v) +1$. The span of $f$ is the largest number in $f(V)$. The radio number of $G$, denoted by $rn(G)$, is the minimum span of a distance labeling for $G$. In this paper, we completely determine the radio numbers for paths and cycles. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 19
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 19255677
- Full Text :
- https://doi.org/10.1137/S0895480102417768