The Shannon Capacity of a Graph
نویسنده
چکیده
This thesis focuses on the Shannon capacity of a graph. Suppose we want to send a message across a channel to a receiver. The general question is about the effective size of an alphabet in a model such that the receiver may recover the original message without errors. To answer this question Shannon defined the Shannon capacity of a graph, Θ(G), and stated Shannon’s Theorem. We study an article of Lovász [5] where he determined the Shannon capacity of the cycle graph C5 and introduced the Lovász Number, an upper bound for the Shannon capacity. About the Lovász Number we define some formulas and prove a couple of theorems. In the last chapter we consider three problems Lovász stated at the end of the article. The problem is that determining the Shannon capacity of a graph, even for very simple graphs, is very difficult. Due to this determining Θ(C7) is still an open problem. Data Title: The Shannon Capacity of a Graph Author: Femke Bekius, [email protected], 5823390 Supervisor: prof. dr. Alexander Schrijver Second assessor: prof. dr. Monique Laurent Enddate: July 22, 2011 Korteweg de Vries Instituut voor Wiskunde Universiteit van Amsterdam Science Park 904, 1098 XH Amsterdam http://www.science.uva.nl/math
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