MATHEMATICA BOHEMICA, Vol. 130, No. 3, pp. 277-282 (2005)

A note on radio antipodal colourings of paths

Riadh Khennoufa, Olivier Togni

Riadh Khennoufa, Olivier Togni, LE2I, UMR 5158 CNRS, Université de Bourgogne, BP 47870, 21078 Dijon cedex, France, e-mail: olivier.togni@

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 (MSC2000): 05C78, 05C12, 05C15

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