Geodesic
A note on radio antipodal colourings of paths
Mathematica Bohemica, Tome 130 (2005) no. 3, pp. 277-282.

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The radio antipodal number of a graph $G$ is the smallest integer $c$ such that there exists an assignment $f\: V(G)\rightarrow \lbrace 1,2,\ldots ,c\rbrace $ satisfying $|f(u)-f(v)|\ge D-d(u,v)$ for every two distinct vertices $u$ and $v$ of $G$, where $D$ is the diameter of $G$. In this note we determine the exact value of the antipodal number of the path, thus answering the conjecture given in [G. Chartrand, D. Erwin and P. Zhang, Math. Bohem. 127 (2002), 57–69]. We also show the connections between this colouring and radio labelings.
DOI : 10.21136/MB.2005.134100
Classification : 05C12, 05C15, 05C78
Keywords: radio antipodal colouring; radio number; distance labeling 
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Khennoufa, Riadh; Togni, Olivier. A note on radio antipodal colourings of paths. Mathematica Bohemica, Tome 130 (2005) no. 3, pp. 277-282. doi : 10.21136/MB.2005.134100. http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134100/

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