The number of edges on generalizations of Paley graphs
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...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201002071 |
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| _version_ | 1832550051330654208 |
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| author | Lawrence Sze |
| author_facet | Lawrence Sze |
| author_sort | Lawrence Sze |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-29a80ef516084abaac27de99f193cfa3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-29a80ef516084abaac27de99f193cfa32025-02-03T06:07:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127211112310.1155/S0161171201002071The number of edges on generalizations of Paley graphsLawrence Sze0Department of Mathematics, California Polytechnic University, San Luis Obispo 93407, CA, USAEvans, 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.http://dx.doi.org/10.1155/S0161171201002071 |
| spellingShingle | Lawrence Sze The number of edges on generalizations of Paley graphs International Journal of Mathematics and Mathematical Sciences |
| title | The number of edges on generalizations of Paley graphs |
| title_full | The number of edges on generalizations of Paley graphs |
| title_fullStr | The number of edges on generalizations of Paley graphs |
| title_full_unstemmed | The number of edges on generalizations of Paley graphs |
| title_short | The number of edges on generalizations of Paley graphs |
| title_sort | number of edges on generalizations of paley graphs |
| url | http://dx.doi.org/10.1155/S0161171201002071 |
| work_keys_str_mv | AT lawrencesze thenumberofedgesongeneralizationsofpaleygraphs AT lawrencesze numberofedgesongeneralizationsofpaleygraphs |