Paley graph:P17: Difference between revisions
(Created page with "{{particular undirected graph}} ==Definition== This graph is defined as the Paley graph <math>P_{17}</math> corresponding to the field of 17 elements.") |
No edit summary |
||
| Line 4: | Line 4: | ||
This graph is defined as the [[Paley graph]] <math>P_{17}</math> corresponding to [[field:F17|the field of 17 elements]]. | This graph is defined as the [[Paley graph]] <math>P_{17}</math> corresponding to [[field:F17|the field of 17 elements]]. | ||
==Graph properties== | |||
{| class="sortable" border="1" | |||
! Property !! Satisfied? !! Explanation | |||
|- | |||
| [[satisfies property::self-complementary graph]] || Yes || [[Paley graphs are self-complementary]] | |||
|- | |||
| [[satisfies property::strongly regular graph]] || Yes || [[Paley graphs are strongly regular]] | |||
|- | |||
| [[satisfies property::regular graph]] || Yes || Follows from being strongly regular. The degree of each vertex is <math>(q - 1)/2 = (17 - 1)/2 = 8</math>. | |||
|- | |||
| [[satisfies property::conference graph]] || Yes || [[Paley graphs are conference graphs]] | |||
|- | |||
| [[satisfies property::symmetric graph]] || Yes || | |||
|- | |||
| [[satisfies property::edge-transitive graph]] || Yes || Follows on account of being Paley | |||
|- | |||
| [[satisfies property::vertex-transitive graph]] || Yes || | |||
|} | |||
Revision as of 04:01, 28 May 2012
This article defines a particular undirected graph, i.e., the definition here determines the graph uniquely up to graph isomorphism.
View a complete list of particular undirected graphs
Definition
This graph is defined as the Paley graph corresponding to the field of 17 elements.
Graph properties
| Property | Satisfied? | Explanation |
|---|---|---|
| self-complementary graph | Yes | Paley graphs are self-complementary |
| strongly regular graph | Yes | Paley graphs are strongly regular |
| regular graph | Yes | Follows from being strongly regular. The degree of each vertex is . |
| conference graph | Yes | Paley graphs are conference graphs |
| symmetric graph | Yes | |
| edge-transitive graph | Yes | Follows on account of being Paley |
| vertex-transitive graph | Yes |
