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

Abstract

In this paper, some algebraic and combinatorial characterizations of the spanning simplicial complex ${\Delta }_s({\mathcal{J}}_{n,m})$ of the Jahangir's graph ${\mathcal{J}}_{n,m}$ are explored. We show that ${\Delta }_s({\mathcal{J}}_{n,m})$ is pure, present the formula for $f$-vectors associated to it and hence deduce a recipe for computing the Hilbert series of the Face ring $k[{\Delta }_s({\mathcal{J}}_{n,m})]$. Finaly, we show that the face ring of ${\Delta }_s({\mathcal{J}}_{n,m})$ is Cohen-Macaulay and give some open scopes of the current work.

arXiv admin note: text overlap with arXiv:1509.04307