Kashif, Agha2018-10-192018-10-192015Anwar, I., Raza, Z., &Kashif, A. (2015). Spanning Simplicial Complexes of Uni-Cyclic Graphs. Algebra Colloquium, 22(04), 707-710.(Agha Kashif) (IF 0.298 JCR Listed)https://escholar.umt.edu.pk/handle/123456789/3372In 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 TreesenMathematics2000 Mathematics Subject Classification: Primary 13P10, Secondary 13H10, 13F20, 13C14Article