Exhibit: graph automorphisms

Here are some larger versions of the figures included at the end of this paper which proves a general Lefschetz fixed point formula for simple graphs.
The mathematica code which computes the Lefschetz number and Zeta function of an arbitrary graph and automorphisms is on the code page.

The complete graph K2

A graph of order 8 with an Z2x Z2 automorphism group.

The cyclic graph C4 with dyhedral group D4 as automorphism group.

The complete graph K3 or triangle with 6 automorphism

A graph with Z2 as automorphism group, the reflection has two triangles invariant.

The automorphism group of the Petersen graph has 120 elements

The automorphism group of the octahedron has 48 elements