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On the Shannon capacity of a graph
Abstract
It is proved that the Shannon zero-error capacity of the pentagon is\sqrt{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 capacity\sqrt{5}.
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Cited by
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Metadata
- Authors
- Lovasz, L.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1979-01
- Volume
- 25
- Issue
- 1
- Pages
- 1-7
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2078289947
- Cited by
- 1,624
- References
- 0
- FWCI
- 12.31
- Type
- journal article
- Language
- en
- Open access
- closed
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- Lovasz, L. (1979). On the Shannon capacity of a graph. IEEE Transactions on Information Theory. https://doi.org/10.1109/tit.1979.1055985
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