A note on radio antipodal colourings of paths. (English) Zbl 1110.05033

Khennoufa, Riadh; Togni, Olivier

Math. Bohem. 130, No. 3, 277-282 (2005).

Summary: The radio antipodal number of a graph \(G\) is the smallest integer \(c\) such that there exists an assignment \(f\: V(G)\rightarrow \{1,2,\dots ,c\}\) 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, 57–69 (2002; Zbl 0995.05056)]. We also show the connections between this colouring and radio labelings.

MSC:

05C15	Coloring of graphs and hypergraphs
05C78	Graph labelling (graceful graphs, bandwidth, etc.)
05C12	Distance in graphs

Keywords:

radio number; distance labeling

Citations:

Zbl 0995.05056