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