Radio labelings of distance graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F13%3A43919556" target="_blank" >RIV/49777513:23520/13:43919556 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.dam.2013.06.024" target="_blank" >http://dx.doi.org/10.1016/j.dam.2013.06.024</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2013.06.024" target="_blank" >10.1016/j.dam.2013.06.024</a>

Result language
angličtina
Original language name
Radio labelings of distance graphs
Original language description
Motivated by the Channel Assignment Problem, we study radio $k$-labelings of graphs. A radio $k$-labeling of a connected graph $G$ is an assignment $c$ of non negative integers to the vertices of $G$ such that $$|c(x) - c(y)| }= k+1 - d(x,y),$$ for any two distinct vertices $x$ and $y$, where $d(x,y)$ is the distance between $x$ and $y$ in $G$. In this paper, we study radio $k$-labelings of distance graphs, i.e., graphs with the set $Z$ of integers as vertex set and in which two distinct vertices $i, j$in $Z$ are adjacent if and only if $|i - j|$ is in $D$. We give some lower and upper bounds for radio $k$-labelings of distance graphs with distance sets $D={1,2,..., t}$, $D={1,t}$ and $D={t-1,t}$ for any positive integer $t}1$.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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