Reconstructible graphs, simplicial flag complexes of homology manifolds and associated right-angled Coxeter groups

Abstract: In this paper, we investigate a relation between finite graphs, simplicial flag complexes and right-angled Coxeter groups, and we provide a class of reconstructible finite graphs. We show that if $\Gamma$ is a finite graph which is the 1-skeleton of some simplicial flag complex $L$ which is a homology manifold of dimension $n \ge 1$, then the graph $\Gamma$ is reconstructible.