Quintic Symmetric Graph

A quintic symmetric graph is a quintic graph (i.e., regular of degree 5) that is also symmetric. Since quintic graphs exist only on an even number of nodes, so do symmetric quintic graphs. The only symmetric quintic graph on 9 or fewer nodes is the complete graph . The following table lists some small symmetric quintic graphs.

graph	nodes
complete graph	6
icosahedral graph	12
Clebsch graph	16