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arXiv · 1311.0981

Spanning Simplicial Ccomplexes of Uni-Cyclic Graphs

Imran Anwar·Zahid Raza·Agha Kashif
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Abstract

In this paper, we introduce the concept of spanning simplicial complexes $Δ_s(G)$ 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 $Δ_s(U_{n,m})$ is shifted hence $Δ_s(U_{n,m})$ is shellable.

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Imran Anwar, Zahid Raza, Agha Kashif. 2013-11-05. Spanning Simplicial Ccomplexes of Uni-Cyclic Graphs. https://doi.org/10.1142/s1005386715000590

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