Riadh Khennoufa, Olivier Togni, LE2I, UMR 5158 CNRS, Universite de Bourgogne, BP 47870, 21078 Dijon cedex, France, e-mail: olivier.togni@
u-bourgogne.fr
Abstract: The radio antipodal number of a graph $G$ is the smallest integer $c$ such that there exists an assignment $f V(G)\rightarrow\{1,2,\ldots,c\}$ satisfying $|f(u)-f(v)|\geq D-d(u,v)$ 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.
Keywords: radio antipodal colouring, radio number, distance labeling
Classification (MSC 2000): 05C78, 05C12, 05C15
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