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Radio labelings of distance graphs

Abstract : 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.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00880024
Contributeur : Olivier Togni <>
Soumis le : mardi 5 novembre 2013 - 11:41:14
Dernière modification le : vendredi 17 juillet 2020 - 14:54:05

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

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