hoffman_singleton_graph¶
- hoffman_singleton_graph()[source]¶
Returns the Hoffman-Singleton Graph.
The Hoffman–Singleton graph is a symmetrical undirected graph with 50 nodes and 175 edges. All indices lie in
Z % 5: that is, the integers mod 5 [1]. It is the only regular graph of vertex degree 7, diameter 2, and girth 5. It is the unique (7,5)-cage graph and Moore graph, and contains many copies of the Petersen graph [2].- Returns
- Gnetworkx Graph
Hoffman–Singleton Graph with 50 nodes and 175 edges
Notes
Constructed from pentagon and pentagram as follows: Take five pentagons \(P_h\) and five pentagrams \(Q_i\) . Join vertex \(j\) of \(P_h\) to vertex \(h·i+j\) of \(Q_i\) [3].
References