SPANNING SIMPLICIAL COMPLEXES OF UNI-CYCLIC GRAPHS

Abstract

In this paper, we introduce the concept of the spanning simplicial complex Δ s (G) associated to a simple finite connected graph G. We characterize all spanning trees of the uni-cyclic graph U n,m . In particular, we give a formula for computing the Hilbert series and h-vector of the Stanley-Reisner ring k[Δ s (U n,m )]. Finally, we prove that the spanning simplicial complex Δ s (U n,m ) is shifted and hence is shellable.