Invariance of the barycentric subdivision of a simplicial complex

Abstract

‎In this paper we prove that a simplicial complex is determined‎ <br />‎uniquely up to isomorphism by its barycentric subdivision as well as‎ <br />‎its comparability graph‎. ‎We also put together several algebraic‎, <br />‎combinatorial and topological invariants of simplicial complexes‎.