Abstract
We study relationships between the diameter D(G), the domination number γ(G), the independence number α(G) and the cop number c(G) of a connected graph G, showing (i.) c(G)≤α(G)−⌊D(G)−32⌋, and (ii.) c(G)≤γ(G)−D(G)3+O(D(G)).
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