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On the Shannon capacity of a graph

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It is proved that the Shannon zero-error capacity of the pentagon issqrt{5}. The method is then generalized to obtain upper bounds on the capacity of an arbitrary graph. A well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases. Several results are obtained on the capacity of special graphs; for example, the Petersen graph has capacity four and a self-complementary graph with n points and with a vertex-transitive automorphism group has capacitysqrt{5}.

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Information Theory, IEEE Transactions on  (Volume:25 ,  Issue: 1 )