  The graph isomorphism problem has a long history in mathematics and computer
science, with applications in computational chemistry and biology, and it is
believed to be neither solvable in polynomial time nor NP-complete. E. Luks
proposed in 1982 the best algorithm so far for the solution of this problem,
which moreover runs in polynomial time if an upper bound for the degrees of the
nodes in the graphs is taken as a constant. Unfortunately, Luks' algorithm is
purely theoretical, very difficult to use in practice, and, in particular, we
have not been able to find any implementation of it in the literature. The main
goal of this paper is to present an efficient implementation of this algorithm
for ternary graphs in the SAGE system, as well as an adaptation to fully
resolved rooted phylogenetic networks on a given set of taxa.
