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The number of edges on generalizations of Paley graphs

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  • Lawrence Sze

Abstract

Evans, Pulham, and Sheenan computed the number of complete 4 -subgraphs of Paley graphs by counting the number of edges of the subgraph containing only those nodes x for which x and x − 1 are quadratic residues. Here we obtain formulae for the number of edges of generalizations of these subgraphs using Gaussian hypergeometric series and elliptic curves. Such formulae are simple in several infinite families, including those studied by Evans, Pulham, and Sheenan.

Suggested Citation

  • Lawrence Sze, 2001. "The number of edges on generalizations of Paley graphs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:979064
    DOI: 10.1155/S0161171201002071
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