  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.
