Search results for "antipodal number"
showing 2 items of 2 documents
Radio k-Labelings for Cartesian Products of Graphs
2005
International audience; Frequency planning consists in allocating frequencies to the transmitters of a cellular network so as to ensure that no pair of transmitters interfere. We study the problem of reducing interference by modeling this by a radio k-labeling problem on graphs: For a graph G and an integer k ≥ 1, a radio k-labeling of G is an assignment f of non negative integers to the vertices of G such that |f(x)−f(y)| ≥ k+1−dG(x,y), for any two vertices x and y, where dG(x,y) is the distance between x and y in G. The radio k-chromatic number is the minimum of max{f(x)−f(y):x,y ∈ V(G)} over all radio k-labelings f of G. In this paper we present the radio k-labeling for the Cartesian pro…
The radio antipodal and radio numbers of the hypercube
2011
International audience; 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.