In this paper, we introduce the concept of spanning simplicial complexes
∆s(G) associated to a simple finite connected graph G. We give the characterization
of all spanning trees of the uni-cyclic graph Un,m. In particular, we
give the formula for computing the Hilbert series and h-vector of the Stanley
Riesner ring k
∆s(Un,m)
. Finally, we prove that the spanning simplicial complex
∆s(Un,m) is shifted hence ∆s(Un,m) is shellable.
Key words : Primary Decomposition, Hilbert Series, f-vectors, h-vectors, spanning
Trees