International Journal of Mathematics and Mathematical Sciences

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International Journal of Mathematics and Mathematical Sciences / 2001 / Article

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Volume 27 |Article ID 979064 | 13 pages | https://doi.org/10.1155/S0161171201002071

The number of edges on generalizations of Paley graphs

Lawrence Sze1

1Department of Mathematics, California Polytechnic University, USA

Received21 Aug 1997

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.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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