ON ISOMORPHISM OF SIMPLICIAL COMPLEXESAND THEIR RELATED ALGEBRAS

Here, we provide a simple proof for the fact that twoSimplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphicas K -algebras. As a consequence, we show that two graphs areisomorphic if and only if their associated edge rings are isomorphicas K-algebras. Based on an explicit K-algebra isomorphism of twoStanley-Reisner rings, or facet rings or edge rings, we present afast algorithm to find explicitly the isomorphism of the associatedsimplicial complexes, or graphs.