Abstract : 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)| \ge 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 (diam(G) − 1)-labeling of G and the radio number is the minimum span of a radio (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.
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00655718 Contributeur : Olivier TogniConnectez-vous pour contacter le contributeur Soumis le : dimanche 1 janvier 2012 - 22:11:28 Dernière modification le : dimanche 26 juin 2022 - 00:42:39
Riadh Khennoufa, Olivier Togni. The radio antipodal and radio numbers of the hypercube. Ars Combinatoria, Waterloo, Ont : Dept. of Combinatorics and Optimization, University of Waterloo, 2011, 102, pp. 447-461. ⟨hal-00655718⟩