I asked this question on MSE a month ago, but nobody was able to answer it, so I guess the question is more difficult than I initially thought: ...
Consider directed graphs where all nodes have 2 inputs and 2 outputs. If we design a box with N inputs and N outputs, what is the smallest number of nodes it must contain to satisfy “pair symmetry” ...
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 ...
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 ...