Mohammed Rafiq Namiq

collaborators

8 papers

math.AC2026

Regularity of Symbolic Powers of Co-Chordal Edge Ideals

Chwas Ahmed, Mohammed Rafiq Namiq

Let $G$ be a finite simple co-chordal graph with at least one edge, and let $I (G)$ be its edge ideal. Over an arbitrary field, we prove that the symbolic powers of $I (G)$ satisfy $…

math.AC2026

Betti Numbers of Sequentially Cohen-Macaulay Co-Chordal Graphs and Their Applications

Mohammed Rafiq Namiq

We study edge ideals of sequentially Cohen-Macaulay co-chordal graphs through the maximal-clique structure of their chordal complements. After making the required construction orde…

math.CO2026

A Complete Classification of 2-Linear Neighborhood Complexes

Mohammed Rafiq Namiq

Let $G$ be a nonempty finite simple graph. We study when the Stanley-Reisner ideal of its neighborhood complex has a $2$ -linear resolution. Combining FrÃ¶berg's theorem with the cl…

math.AC2026

Vertex Dismissibility and Scalability of Simplicial Complexes

Mohammed Rafiq Namiq

We introduce and study strongly vertex dismissible, vertex dismissible, and scalable simplicial complexes as non-pure extensions of vertex decomposability and shellability. Strong…

math.AC2026

Explicit Betti Numbers for Skeletons of Chordal Clique Complexes and Their Alexander Duals

Mohammed Rafiq Namiq

We study the homological properties of $I^_{r} (n_{1}, \dots, n_{e})$ , a simplicial complex formed by sequentially gluing complete graphs along $(r_{i} - 1)$ -simplices. This constr…

math.AC2025

Initially Cohen-Macaulay Modules

Mohammed Rafiq Namiq

In this paper, we introduce initially Cohen-Macaulay modules over a commutative Noetherian local ring $R$ , a new class of $R$ -modules that generalizes both Cohen-Macaulay and seque…