Journal of Prime Research in Mathematics

# On algebraic aspects of SSC associated to the subdivided prism graph

Mehwish Javed$$^a$$, Agha Kashif$$^a$$, Muhammad Javaid$$^{a,*}$$
$$^a$$Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan.
In this article, some important combinatorial and algebraic properties of spanning simplicial complex associated to the subdivided prism graph $$P(n,m)$$ are presented. The $${f}-$$vector of the spanning simplicial complex $$\Delta_s(P(n,m))$$ and the Hilbert series for the face ring $$K\big[\Delta_s(P(n,m))\big]$$ are computed. Further, the associated primes of the facet ideal $$I_{\mathcal{F}}(\Delta_s(P(n,m)))$$ are determined. Finally, the Cohen-Macaulay characterization of the SR-ring of $$\Delta_s(P(n,m))$$ is discussed.
Simplicial Complexes, $${f}-$$vector, Spanning Trees, Face Ring, Hilbert Series, Cohen Macaulay.