Perfect codes in graphs |
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Authors: | Norman Biggs |
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Institution: | Royal Holloway College, University of London, Egham, Surrey, England |
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Abstract: | The classical problem of the existence of perfect codes is set in a vector space. In this paper it is shown that the natural setting for the problem is the class of distance-transitive graphs. A general theory is developed that leads to a simple criterion for the existence of a perfect code in a distance-transitive graph, and it is shown that this criterion implies Lloyd's theorem in the classical case. |
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