8 citations · 21 across the 25 of their papers we have counts for
17 papers · 1 filter
Metric Bases of Barycentric and Matching Subdivisions of Zero-Divisor Graphs
Vidya S, Prasanna Poojary, Bilal Ahmad Rather +1
In this paper, we study metric bases and related metric properties for barycentric and partial matching subdivisions of the zero-divisor graph of , where and $q…
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_…
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--Reisner…
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 $…
Betti numbers for cochordal zero-divisor graphs of commutative rings
Bilal Ahmad Rather
This paper studies the zero-divisor graphs attached to several finite chain-ring families and computes the homological invariants of their edge ideals by using cochordal constructi…
Vertex connectivity of the nonzero nonunit core of the comaximal graph of
Bilal Ahmad Rather
This article settles Problem 7.2 posed by [Banerjee, Special Matrices (2022)] for the induced subgraph of the comaximal graph when is squarefree. Let $n=…
On roots of domination polynomials for friendship and book graphs
Bilal Ahmad Rather
This study examines the domination polynomials of friendship graphs and book graphs, focusing on unanswered questions related to these families [Alikhani, Brown and Jahari, on the…
On (distance) Laplacian characteristic polynomials of power graphs
Bilal Ahmad Rather, Mustapha Aouchiche, Victor A. Bovdi
The characteristic polynomials of the Laplacian and the distance Laplacian matrices of power graphs of groups of order , where and are { primes,} are obtained.…
Independent domination polynomial of comaximal graphs of commutative rings
Bilal Ahmad Rather
The comaximal graph of a commutative ring is a simple graph with vertex set and two distinct vertices and of are adjacent if and only if $ aR…
On the quotient matrix and its distinct eigenvalues
Bilal Ahmad Rather, Jianfeng Wang, Zhaoxi Li
Let be an matrix partitioned into blocks according to a partition of its index set, and let be the corresponding equitable quotient…
Spectral Properties of Zero-Divisor Graphs of Truncated Polynomial Rings
Bilal Ahmad Rather
Let be a commutative ring with identity and let denote the set of nonzero zero-divisors of . The \emph{zero-divisor graph} is the simple graph…
Block Structure and Spectrum of Zero-Divisor Graphs of Lipschitz Quaternion Rings Modulo
Bilal Ahmad Rather
We study the adjacency spectra of zero-divisor graphs associated with Lipschitz quaternion rings modulo . For an odd prime , the identification $\mathbb{L}_p\cong M_2(\mathbb…
Domination polynomial of co-maximal graphs of integer modulo ring
Bilal Ahmad Rather
We investigate the domination polynomial of the co-maximal graph related to the ring of integers modulo . Explicit formulas are derived for \( n = p^{n_1} \) a…
Degree-based weighted adjacency matrices: spectra, integrality, and edge deletion effects
Bilal Ahmad Rather, Hilal Ahmad Ganie
We study degree-based weighted adjacency matrices associated with symmetric edge-weight functions , with emphasis on complete multipartite graphs and spectral changes c…
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…