Abstract

The following result is established: Given a group $H$, there exists an $r$-regular graph $G$ such that every subgroup of $H$ (including $H$ itself) is isomorphic to the group $\Aut(G,\varphi)$ of all automorphisms preserving a certain proper $r$-edge-colouring $\varphi$ of $G$. If the group is finite, so is the graph.

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