The SSC of the Generalised Jahangir's Graph Jm,k and its Algebraic Characterizations

Abstract

In this article, we present important combinatorial and algebraic properties of spanning simplicial complex (SSC) of the generalised Jahangir’s graph Jm,k. We describe the relation to find f−vectors associated to ∆s(Jm,k) and determine the Hilbert series for the SR-ring K∆s(Jm,k). In the end, we present the associated primes of the facet ideal IF (∆s(Jm,k)) and the Cohen-Macaulay characterization of the SR-ring of ∆s(Jm,k).