S. Pirzada

activity

20212026

most citedOn

A_{α}

-spectrum of joined union of graphs and its applications to power graphs of finite groups

2 citations · 4 across the 8 of their papers we have counts for

collaborators

11 papers

math.RA2026

Multiplicity-One Structure in Graded Zero-Divisor Graphs

M. Aijaz, Shahnawaz A. Rather, S Pirzada

Let $H$ be a multiplicative group, $R$ a commutative $H$-graded ring, and $M$ a nonzero finitely generated gr-semisimple $H$-graded $R$-module. We assume that $M$ adm…

math.AC2026

Binomial edge ideals of bipartite complements of even cycles

Shahnawaz Ahmad Rather, S. Pirzada, M. Aijaz

Let $G_{n}$ be the bipartite complement of the even cycle $C_{2 n}$ , and let $J_{G_{n}}$ be its binomial edge ideal. For $n \geq 5$ , we study the interaction between the combinatorial str…

math.AC2026

Homological invariants of Edge Ideals associated to powers of cycles

Shahnawaz Ahmad Rather, S. Pirzada, M. Aijaz

Let $G_{n,m}=\overline{\C_n^{[m]}}$, where $\C_n^{[m]}$ denotes the closed $m$ th power of the $n$ -cycle. We study the graded Betti numbers and homological invariants of the edge ri…

math.CO2026

On distance integral and distance Laplacian integral graphs

S. Pirzada, Ummer Mushtaq, Leonardo de Lima

Let $G$ be a connected graph on $n$ vertices and let $D (G)$ and $D^{L} (G)$ be the distance and the distance Laplacian matrices associated with $G$ . A graph $G$ is said to be $D$ -in…

math.CO2026

The spectral extrema of graphs of odd size forbidding $H (4, 3)$ beyond the book graph

Abdul Basit Wani, S. Pirzada, Amir Rehman

A graph is said to be $H$ -free if it does not contain a subgraph isomorphic to $H$ . The fish graph, denoted by $H (4, 3)$ , is a $6 -$ vertex graph obtained from a cycle of length $4$ …

math.CO2025

On connected graphs with finite spectral redundancy index and Pythagorean triplets

Pawan Kumar, S. Pirzada, S. Merajuddin

This article investigates spectral redundancy, a concept initially introduced by Alberto Seeger. Spectral redundancy arises when different connected induced subgraphs of a graph sh…

math.SP2023

On the eigenvalues and energy of the $A_{α}$ -matrix of graphs

Nijara Konch, A. Bharali, S. Pirzada

For a graph $G$ , the generalized adjacency matrix $A_{α} (G)$ is the convex combination of the diagonal matrix $D (G)$ and the adjacency matrix $A (G)$ and is defined as $A_α(G)=αD(G)+(…

math.CO2022★ 1 cited

On distance Laplacian spread and Wiener index of a graph

Saleem Khan, S. Pirzada

Let $G$ be a simple connected simple graph of order $n$ . The distance Laplacian matrix $D^{L} (G)$ is defined as $D^{L} (G) = D ia g (T r) - D (G)$ , where $D ia g (T r)$ is the diagonal matrix of v…

math.CO2022

On the distribution of eigenvalues of the reciprocal distance Laplacian matrix of graphs

S. Pirzada, Saleem Khan

The reciprocal distance Laplacian matrix of a connected graph $G$ is defined as $R D^{L} (G) = R T (G) - R D (G)$ , where $R T (G)$ is the diagonal matrix of reciprocal distance degrees and $RD(G…

math.CO2022★ 1 cited

Distance Laplacian eigenvalues of graphs and chromatic and independence number

S. Pirzada, Saleem Khan

For a connected graph $G$ of order $n$ , let $D ia g (T r)$ be the diagonal matrix of vertex transmissions and $D (G)$ be the distance matrix of $G$ . The distance Laplacian matrix of $G$ …

math.CO2021★ 2 cited

On $A_{α}$ -spectrum of joined union of graphs and its applications to power graphs of finite groups

Bilal A. Rather, Hilal A. Ganie, S. Pirzada

For a simple graph $G$ , the generalized adjacency matrix $A_{α} (G)$ is defined as $A_{α} (G) = α D (G) + (1 - α) A (G), α \in [0, 1]$ , where $A (G)$ is the adjacency matrix and $D (G)$ is the diagona…