Independence and coloring properties of direct products of some vertex-transitive graphs

Let @a(G) and @g(G) denote the independence number and chromatic number of a graph G, respectively. Let GxH be the direct product graph of graphs G and H. We show that if G and H are circular graphs, Kneser graphs, or powers of cycles, then @a(GxH)=max{@a(G)|V(H)|,@a(H)|V(G)|} and @g(GxH)=min{@g(G),@g(H)}.

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