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 javaidmath@gmail.com

Copyright © 2021 Mehwish Javed, Agha Kashif, Muhammad Javaid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 1 September 2020; Accepted: 25 February 2021; Published Online: 30 March 2021.

Abstract

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.

Keywords:

Simplicial Complexes, \({f}-\)vector, Spanning Trees, Face Ring, Hilbert Series, Cohen Macaulay.