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Highly symmetric 6-regular graph with 20 vertices
I'm interested in (node/edge-)symmetric 6-regular graphs on 20 vertices and 60 edges, especially ones with a A5/icosahedral/dodecahedral symmetry group and especially their chromatic number. … Is the shape governed by subgroups of the symmetry group?
Thank you in advance for any hint :-)
OLD QUESTION FOR THE FIRST GRAPH. …