  Let $R_m$ be the (unique) universal homogeneous $m$-edge-coloured countable
complete graph ($m\ge2$), and $G_m$ its group of colour-preserving
automorphisms. The group $G_m$ was shown to be simple by John Truss. We examine
the automorphism group of $G_m$, and show that it is the group of permutations
of $R_m$ which induce permutations on the colours, and hence an extension of
$G_m$ by the symmetric group of degree $m$. We show further that the extension
splits if and only if $m$ is odd, and in the case where $m$ is even and not
divisible by~$8$ we find the smallest supplement for $G_m$ in its automorphism
group.
  (This unpublished paper from 2007 is placed here because of renewed interest
in the topic.)

Combinatorics;Group Theory