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Radio k-colorings of paths

2004
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Discussiones Mathematicae Graph Theory
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For a connected graph G of diameter d and an integer k with 1 ≤ k ≤ d, a radio k-coloring of G is an assignment c of colors (positive integers) to the vertices of G such that d(u, v) + |c(u) − c(v)| ≥ 1 + k for every two distinct vertices u and v of G, where d (u, v) is the distance between u and v. The value rc k (c) of a radio k-coloring c of G is the maximum color assigned to a vertex of G. The radio k-chromatic number rc k (G) of G is the minimum value of rc k (c) taken over all radio

doi:10.7151/dmgt.1209
fatcat:epxlr4nhlbadfalrxtcrjkbyyy