  Graph isomorphism is an important problem as its worst-case time complexity
is not yet fully understood. In this study, we try to draw parallels between a
related optimization problem called point set registration. A graph can be
represented as a point set in enough dimensions using a simplex embedding and
sampling. Given two graphs, the isomorphism of them corresponds to the
existence of a perfect registration between the point set forms of the graphs.
In the case of non-isomorphism, the point set form optimization result can be
used as a distance measure between two graphs having the same number of
vertices and edges. The related idea of equivalence classes suggests that graph
canonization may be an important tool in tackling graph isomorphism problem and
an orthogonal transformation invariant feature extraction based on this high
dimensional point set representation may be fruitful. The concepts presented
can also be extended to automorphism, and subgraph isomorphism problems and can
also be applied on hypergraphs with certain modifications.
