  The computational complexity of the graph isomorphism problem is considered
to be a major open problem in theoretical computer science. It is known that
testing isomorphism of chordal graphs is polynomial-time equivalent to the
general graph isomorphism problem. Every chordal graph can be represented as
the intersection graph of some subtrees of a representing tree, and the leafage
of a chordal graph is defined to be the minimum number of leaves in a
representing tree for it. We prove that chordal graph isomorphism is fixed
parameter tractable with leafage as parameter. In the process we introduce the
problem of isomorphism testing for higher-order hypergraphs and show that
finding the automorphism group of order-$k$ hypergraphs with vertex color
classes of size $b$ is fixed parameter tractable for any constant $k$ and $b$
as fixed parameter.
