I have posted a diagram, showing as much of the symmetry of this graph as planar representation allows, at https://www.dropbox.com/s/aeea6bqlrt23tck/semi_6x6.png Note the 4-fold diagonal coincidences --- whereby hangs another tale entirely! Fred Lunnon On 4/14/14, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Since you dispatched 4x4 so readily, perhaps you can manage something about the graph genus 6x6 knight moves on a torus instead?
In the 4x4 case the vertices had valency 4 instead of 8 . The 6x6 case degenerates as well, less predictably: vertices opposite across the torus have all neighbours in common; identification yields 18 vertices and 36 edges and valency 4 immersed on a Klein bottle. The symmetry group has order 144 .
Fred Lunnon