Universality for Barycentric subdivision

Invariance of the barycentric subdivision of a simplicial complex

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

The Γ-vector of a Barycentric Subdivision

We prove that the γ-vector of the barycentric subdivision of a simplicial sphere is the f -vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the h-vector of the barycentric subdivision of a boolean complex.

f-VECTORS OF BARYCENTRIC SUBDIVISIONS

For a simplicial complex or more generally Boolean cell complex ∆ we study the behavior of the f and h-vector under barycentric subdivision. We show that if ∆ has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney-Davis conjecture for spheres that are the subdivision of a Bool...

Computing Solid Angles by Barycentric Subdivision ∗

Cordial Labeling in Context of Barycentric Subdivision of Special Graphs

In this paper we discuss cordial labeling in context of barycentric subdivision of shell graph, complete bipartite graph Kn,n and wheel graph. AMS subject classification: 05C78.