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.
Correspondence should be addressed to: Muhammad Javaid at


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.