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For a simple graph G with chromatic number x(G), the Nordhaus-Gaddum inequalities give upper and lower bounds for z(G) • (G ¢) and z(G)+ x(GC). Based on a characterization by Fink of the extremal graphs G attaining the lower bounds for the product and sum, we characterize the extremal graphs G for which A(G)B(G c) is minimum, where A and B are each of… (More)

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