Spanning Simplicial Ccomplexes of Uni-Cyclic Graphs

Abstract

In this paper, we introduce the concept of spanning simplicial complexes ${\Delta }_s(G)$ associated to a simple finite connected graph G. We give the characterization of all spanning trees of the uni-cyclic graph $U_{n,m}$. In particular, we give the formula for computing the Hilbert series and h-vector of the Stanley-Riesner ring k[Δ_s(U_{n,m})]. Finally, we prove that the spanning simplicial complex ${\Delta }_s(U_{n,m})$ is shifted hence ${\Delta }_s(U_{n,m})$ is shellable.

to appear in Algebra Colloquium. This paper is included in the Ph.D thesis of the third author

Cited by in corpus (1)

• On Algebraic Characterization of SSC of the Jahangir's Graph ${\mathcal{J}}_{n,m}$