Journal ArticleDOI
On the Shannon capacity of a graph
TLDR
It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and 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.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} .read more
Citations
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References
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Journal ArticleDOI
The zero error capacity of a noisy channel
TL;DR: It is shown that while the ordinary capacity of a memoryless channel with feedback is equal to that of the same channel without feedback, the zero error capacity may be greater and a solution is given to the problem of evaluating C_oF.
Journal ArticleDOI
Intersection theorems for systems of finite sets
Paul Erdös,Chao Ko,Richard Rado +2 more
TL;DR: In this article, the obliteration operator is used to remove from any system of elements the element above which it is placed, and the set of all systems (ao,av...,dn) such that avc[0,m); \av\ 1 (v < »),
Journal ArticleDOI
On a problem of c. e. shannon in graph theory
TL;DR: In this paper, the authors define the notion of clique as a subset of vertices such that no two different vertices in the subset are joined by an edge in the complete subgraph.