16 papers
Homological invariants of edge ideals of the multiple extended complete split-like graphs
Bilal Ahmad Rather
We study the graphs $MECS_{b,n}^a \cong \overline{K}_a \join \big(n(K_b+K_2)\big)$, obtained by attaching an independent set of size to disjoint copies of the block $K_b+K_…
Explicit Formulas and Unimodality Phenomena for General Position Polynomials
Bilal Ahmad Rather
The general position problem in graphs seeks the largest set of vertices such that no three vertices lie on a common geodesic. Its counting refinement, the general position polynom…
Graded Betti numbers of generalized split--join graphs and applications
Bilal Ahmad Rather
We determine the full graded Betti tables of graph families that subsume several classes studied recently in the literature, namely the generalized multiple complete split-like gra…
Combinatorial and analytic aspects of independence polynomials of zero divisor graphs
Bilal Ahmad Rather
The independence polynomial of a graph encapsulates all independent sets of differing sizes, a task classified as NP-hard in theoretical computer science. This article examines the…
The NF-operator and the NF-Numbers of Simplicial Complexes
Bilal Ahmad Rather
Let be a simplicial complex and let denote the NF-operator. The NF-complex is defined as the Stanley--Reisn…
Extremal chromatic bounds for distance Laplacian eigenvalues
Bilal Ahmad Rather
For a connected simple graph on vertices with chromatic number , the distance Laplacian matrix is $\DL(G)=\operatorname{diag}(\Tr_G(v_1),\dots,\Tr_G(v_n))-D(G)$, where…