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The radio antipodal and radio numbers of the hypercube. (English) Zbl 1265.05536

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.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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