On Algebraic Characterization Of Ssc Of The Jahangir'S Graph J(N,M)

In this paper, some algebraic and combinatorial characterizations of the spanning simplicial complex Delta(s)(J(n,m)) of the Jahangir's graph J(n,m) are explored. We show that Delta(s)(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)(J(n,m))]. Finally, we show that the face ring of Delta(s)(J(n,m)) is Cohen-Macaulay and give some open scopes of the current work.