6
votes
5answers
1k views

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. So far I ...
3
votes
2answers
420 views

Does graph asymmetry imply all eigenvalues of the graph Laplacian are simple?

It is well known that 1) if there exists a non-trivial automorphism of a graph $G$ with corresponding permutation matrix $P$ then if $(v,\lambda)$ is an eigenvector-eigenvalue pair of the graph ...