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

Abstract

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

Keywords

• simplicial complexes
• spanning trees
• face ring
• hilbert series
• f-vectors
• cohen macaulay
• 13p10
• 13h10
• 13f20
• 13c14