Khennoufa, Riadh; Togni, Olivier The radio antipodal and radio numbers of the hypercube. (English) Zbl 1265.05536 Ars Comb. 102, 447-461 (2011). Summary: A radio \(k\)-labeling of a connected graph \(G\) is an assignment \(f\) of non negative integers to the vertices of \(G\) such that \(| f(x)-f(y)| \geq k+1-d(x,y)\) for any two vertices \(x\) and \(y\), where \(d(x,y)\) is the distance between \(x\) and \(y\) in \(G\). The radio antipodal number is the minimum span of a radio \((\operatorname{diam}(G)-1)\)-labeling of \(G\) and the radio number is the minimum span of a radio \((\operatorname{diam}(G))\)-labeling of \(G\). In this paper, the radio antipodal number and the radio number of the hypercube are determined by using a generalization of binary Gray codes. Cited in 24 Documents MSC: 05C78 Graph labelling (graceful graphs, bandwidth, etc.) Keywords:graph labeling; radio antipodal number; radio number; generalized binary Gray code PDFBibTeX XMLCite \textit{R. Khennoufa} and \textit{O. Togni}, Ars Comb. 102, 447--461 (2011; Zbl 1265.05536)