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Article Dans Une Revue Discrete Applied Mathematics Année : 2013

Radio labelings of distance graphs

Roman Čada
  • Fonction : Auteur
Jan Ekstein
  • Fonction : Auteur
Premysl Holub
  • Fonction : Auteur


Motivated by the Channel Assignment Problem, we study radio k-labelings of graphs. A radio k-labeling of a connected graph G is an assignment c of non-negative integers to the vertices of G such that |c(x)−c(y)|≥k+1−d(x,y), for any two vertices x and y, x≠y, where d(x,y) is the distance between x and y in G. In this paper, we study radio k-labelings of distance graphs, i.e., graphs with the set Z of integers as vertex set and in which two distinct vertices i,j∈Z are adjacent if and only if |i−j|∈D. We give some lower and upper bounds for radio k-labelings of distance graphs with distance sets D(1,2,...,t), D(1,t) and D(t−1,t) for any positive integer t>1.

Dates et versions

hal-00880024 , version 1 (05-11-2013)



Roman Čada, Jan Ekstein, Premysl Holub, Olivier Togni. Radio labelings of distance graphs. Discrete Applied Mathematics, 2013, 161 (18), pp.2876-2884. ⟨10.1016/j.dam.2013.06.024⟩. ⟨hal-00880024⟩
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