  Graph C*-algebras have been celebrated as C*-algebras that can be seen,
because many important properties may be determined by looking at the
underlying graph. This paper introduces the permutation graph for a permutative
endomorphism of a graph C*-algebra as a labeled directed multigraph that gives
a visual representation of the endomorphism and facilitates computations.
Combinatorial criteria have previously been developed for deciding when such an
endomorphism is an automorphism, but here the question is reformulated in terms
of the permutation graph and new proofs are given. Furthermore, it is shown how
to use per- mutation graphs to efficiently generate exhaustive collections of
permutative automorphisms. Permutation graphs provide a natural link to the
textile systems representing induced endo- morphisms on the edge shift of the
given graph, and this allows the powerful tools of the theory of textile
systems developed by Nasu to be applied to the study of permutative
endomorphisms.
