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Let G be a finite simple graph. For an integer k≥1, a radio k-coloring of G is an assignment f of non-negative integers to the vertices of G satisfying the condition ∣f(u)−f(v)∣≥k+1−d(u,v) for any two distinct vertices u, v of G. The span of f is the largest integer assigned to a vertex of G by f and radio k-chromatic number of G, denoted by rck(G), is the minimum span over all radio k-colorings of...
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