Hoffman–Singleton graph

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The two circles shaped Hoffman–Singleton graph and its component (50 + 25 + 25 + 25 + 25 + 25 = 175 edges).

The Hoffman–Singleton graph is a graph with the following properties:

• The graph has 50 vertices.
• The graph has 175 edges.
• The graph has a vertex degree of 7.
• The graph has a diameter of 2.
• The graph has a girth of 5.

Therefore, the graph is the following:

• strongly regular.
• A Moore graph.
• An integral graph.
• A symmetric graph.
• The (7,5)-cage.

A Hoffman–Singleton graph is the highest order Moore graph to be found, and all Hoffman–Singleton graphs will adhere to all eight properties listed above—no matter how they are drawn.

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