arXiv subjects

Agha Kashif

Publications and source records attributed to Agha Kashif.

4 recordsLinked to original sources

arXiv2017

On Algebraic Characterization of SSC of the Jahangir's Graph $\mathcal{J}_{n,m}$

In this paper, some algebraic and combinatorial characterizations of the spanning simplicial complex $Δ_s(\mathcal{J}_{n,m})$ of the Jahangir's graph $\mathcal{J}_{n,m}$ are explored. We show that $Δ_s(\mathcal{J}_{n,m})$ 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 $k[Δ_s(\mathcal{J}_{n,m})]$. Finaly, we show that the face ring of $Δ_s(\mathcal{J}_{n,m})$ is Cohen-Macaulay and give some open scopes of the current work.

math.AC↗

arXiv2016

Algebraic characterization of the SSC $Δ_s(\mathcal{G}_{n,r}^{1})$

In this paper, we characterize the set of spanning trees of $\mathcal{G}_{n,r}^1$ (a simple connected graph consisting of $n$ edges, containing exactly one $1$-edge-connected chain of $r$ cycles $\mathbb{C}_r^1$ and $\mathcal{G}_{n,r}^{1}\setminus\mathbb{C}_r^1$ is a forest). We compute the Hilbert series of the face ring $k[Δ_s (\mathcal{G}_{n,r}^1)]$ for the spanning simplicial complex $Δ_s (\mathcal{G}_{n,r}^1)$. Also, we characterize associated primes of the facet ideal $I_{\mathcal{F}} (Δ_s (\mathcal{G}_{n,r}^1))$. Furthermore, we prove that the face ring $k[Δ_s(\mathcal{G}_{n,r}^{1})]$ is Cohen-Macaulay.

math.AC↗

arXiv2015

Topology On BCK-Modules

In this paper, we introduce the notion of a BCK-topological module in a natural way and establish that every decreasing sequence of submodules on a BCK-module M over bounded commutative BCK-algebra X is indeed a BCK- topological module. We have defined the notion of compatible and strict BCK- module homomorphisms, and establish that a strict BCK-module homomorphism is an open as well as a continuous mapping. Also, we establish the necessary and sufficient condition for a compatible mapping to be strict.

math.GM↗

arXiv2013

Spanning Simplicial Ccomplexes of Uni-Cyclic Graphs

In this paper, we introduce the concept of spanning simplicial complexes $Δ_s(G)$ associated to a simple finite connected graph G. We give the characterization of all spanning trees of the uni-cyclic graph $U_{n,m}$. In particular, we give the formula for computing the Hilbert series and h-vector of the Stanley-Riesner ring k[Δ_s(U_{n,m})]. Finally, we prove that the spanning simplicial complex $Δ_s(U_{n,m})$ is shifted hence $Δ_s(U_{n,m})$ is shellable.

math.AC↗