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

On algebraic characterization of SSC of the Jahangir’s graph 𝓙 n , m