K<sub>7</sub> diagram, © Wikipedia
K<sub>7</sub> diagram, © N.S.Wedd
K<sub>7</sub> diagram, © N.S.Wedd


It has degree 6, with 7 vertices and 21 edges.
It has girth 3, diameter 1 and radius 1.
Its symmetry group is S7, with 5040 elements.
It is not bipartite.
It is Hamiltonian.
It is symmetric.
It is 6-arc-transitive.

Regular maps

K7 is the skeleton of {3,6}(1,3)

Dual graphs

K7 is the dual of Heawood graph in the torus

For copyright details of Wikipedia image see   Complete_graph_K7.svg.

Lists of Graphs
Index to Regular Maps