S. Pirzada

activity

20062026

most citedOn

α

-adjacency energy of graphs and Zagreb index

8 citations · 26 across the 29 of their papers we have counts for

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27 papers · 1 filter

math.CO2026

Graphs with ${P_{3}, P_{4}, P_{5}}$ -factors in terms of size and spectral radius

Zahoor Iqbal Bhat, S. Pirzada

Let $G$ be a connected graph of order $n$ . A ${P_{3}, P_{4}, P_{5}}$ -factor is a spanning subgraph $H$ of $G$ such that every component of $H$ is isomorphic to an element of $\{P_3,P_4,P…

math.CO2024

On the spectral redundancy of pineapple graphs

Pawan Kumar, S. Pirzada, Merajuddin +1

In this article, we explore the concept of spectral redundancy within the class of pineapple graphs, denoted as $P (α, β)$ . These graphs are constructed by attaching $β$ pe…

math.CO2024

On maximum spectral radius of ${H (3, 3), H (4, 3)}$ -free graphs

Amir Rehman, S. Pirzada

Let $G$ be a simple connected graph of size $m$ . Let $A$ be the adjacency matrix of $G$ and let $ρ (G)$ be the spectral radius of $G$ . A graph is said to be $H$ -free if it does not…

math.CO2023

Direct sum graph of the subspaces of a finite dimensional vector space over finite fields

Bilal A. Wani, Aaqib Altaf, S. Pirzada +1

In this paper, we introduce a new graph structure, called the $d i r ec t s u m g r a p h$ on a finite dimensional vector space. We investigate the connectivity, diameter and the completen…

math.CO2023

On the Estrada index of unicyclic and bicyclic signed graphs

Tahir Shamsher, S. Pirzada, Mushtaq A. Bhat

Let $Γ = (G, σ)$ be a signed graph of order $n$ with eigenvalues $μ_{1}, μ_{2}, \dots, μ_{n} .$ We define the Estrada index of a signed graph $Γ$ as $E E (Γ) = \sum_{i = 1}^{n} e^{μ_{i}}$ . We characteri…

math.CO2023

Spectra of s-neighbourhood corona of two signed graphs

Tahir Shamsher, Mir Riyaz ul Rashid, S. Pirzada

A signed graph $S = (G, σ)$ is a pair in which $G$ is an underlying graph and $σ$ is a function from the edge set to ${\pm 1}$ . For signed graphs $S_{1}$ and $S_{2}$ on $n_{1}$ and…

math.CO2022

On adjacency and Laplacian cospectral non-isomorphic signed graphs

Tahir Shamsher, S. Pirzada, Mushtaq A. Bhat

Let $Γ = (G, σ)$ be a signed graph, where $σ$ is the sign function on the edges of $G$ . In this paper, we use the operation of partial transpose to obtain non-isomorphic Laplacian cos…

math.CO2022

On Zagreb index, signless Laplacian eigenvalues and signless Laplacian energy of a graph

S. Pirzada, Saleem Khan

Let $G$ be a simple graph with order $n$ and size $m$ . The quantity $M_{1} (G) = i = 1 \sum n d_{v_{i}}^{2}$ is called the first Zagreb index of $G$ , where $d_{v_{i}}$ is the de…

math.CO2022

On graphs with distance Laplacian eigenvalues of multiplicity $n - 4$

Saleem Khan, S. Pirzada

Let $G$ be a connected simple graph with $n$ vertices. 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 ver…

math.CO2021

On distance Laplacian energy in terms of graph invariants

Hilal A. Ganie, Rezwan Ul Shaban, Bilal A. Rather +1

For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues $ρ_{1}^{L} \geq ρ_{2}^{L} \geq \dots \geq ρ_{n}^{L}$ , the distance Laplacian energy $D L E (G)$ is…

math.CO2021

On the eigenvalues of signed complete bipartite graphs

S. Pirzada, Tahir Shamsher, Mushtaq A. Bhat

Let $Γ = (G, σ)$ be a signed graph, where $σ$ is the sign function on the edges of $G$ . The adjacency matrix of $Γ = (G, σ)$ is a square matrix $A (Γ) = A (G, σ) = (a_{ij}^{σ})$ , wh…

math.CO2021

On a conjecture of Laplacian energy of trees

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

Let $G$ be a simple graph with $n$ vertices, $m$ edges having Laplacian eigenvalues $μ_{1}, μ_{2}, \dots, μ_{n - 1}, μ_{n} = 0$ . The Laplacian energy $L E (G)$ is defined as $LE(G)=\sum_{i=1}^{…

math.CO2021

On normalized Laplacian eigenvalues of power graphs associated to finite cyclic groups

Bilal A. Rather, S. Pirzada, T. A. Chishti +1

For a simple connected graph $G$ of order $n$ , the normalized Laplacian is a square matrix of order $n$ , defined as $\mathcal{L}(G)= D(G)^{-\frac{1}{2}}L(G)D(G)^{-\frac{1}{2}…

math.CO2020

Sphere of Influence Dimension Conjecture 'Almost Proved'

Surinder Pal Singh Kainth, Ramanjit Kumar, S. Pirzada

The sphere-of-influence graph (SIG) on a finite set of points in a metric space, each with an open ball centred about it of radius equal to the distance between that point and its…

math.CO2020★ 8 cited

On $α$ -adjacency energy of graphs and Zagreb index

S. Pirzada, Bilal A. Rather, Hilal A. Ganie +1

Let $A (G)$ be the adjacency matrix and $D (G)$ be the diagonal matrix of the vertex degrees of a simple connected graph $G$ . Nikiforov defined the matrix $A_{α} (G)$ of the convex comb…

math.CO2019

On spectral spread of generalized distance matrix of a graph

Hilal A. Ganie, S. Pirzada, A. Alhevaz +1

For a simple connected graph $G$ , let $D (G)$ , $T r (G)$ , $D^{L} (G)$ and $D^{Q} (G)$ , respectively be the distance matrix, the diagonal matrix of the vertex transmissions, distance Lap…

math.CO2018

Mixing Time of Markov chain of the Knapsack Problem

Koko K. Kayibi, S. Pirzada, Carrie Rutherford

To find the number of assignments of zeros and ones satisfying a specific Knapsack Problem is $# P$ hard, so only approximations are envisageable. A Markov chain allowing uniform s…

math.CO2015

Spectra and energy of bipartite signed digraphs

Mushtaq A. Bhat, S. Pirzada

The set of distinct eigenvalues of a signed digraph $S$ together with their multiplicities is called its spectrum. The energy of a signed digraph $S$ with eigenvalues $z_1,z_2,\cdo…

math.CO2013★ 3 cited

On the construction of l-equienergetic graphs

S. Pirzada, Hilal A Ganie

For a graph with $n$ vertices and $m$ edges, having Laplacian spectrum $μ_{1}, μ_{2}, \dots, μ_{n}$ and signless Laplacian spectrum $μ_{1}^{+}, μ_{2}^{+}, \dots, μ_{n}^{+}$ , the Laplacian energy and…

math.CO2013

Energy, Laplacian energy of double graphs and new families of equienergetic graphs

S. Pirzada, Hilal A Ganie

For a graph $G$ with vertex set $V (G) = {v_{1}, v_{2}, \dots, v_{n}}$ , the extended double cover $G^{*}$ is a bipartite graph with bipartition (X, Y), $X = {x_{1}, x_{2}, \dots, x_{n}}$ and $Y…

math.CO2013

Energy of signed digraphs

S. Pirzada, Mushtaq A. Bhat

In this paper we extend the concept of energy to signed digraphs. We obtain Coulson's integral formula for energy of signed digraphs. Formulae for energies of signed directed cycle…

math.CO2010★ 3 cited

Imbalances in directed multigraphs

S. Pirzada, T. A. Naikoo, U. Samee +1

In a directed multigraph, the imbalance of a vertex $v_{i}$ is defined as $b_{v_{i}} = d_{v_{i}}^{+} - d_{v_{i}}^{-}$ , where $d_{v_{i}}^{+}$ and $d_{v_{i}}^{-}$ denote the outdegree an…

math.CO2006

Kings and serfs in oriented graphs

S. Pirzada, N. A. Shah

In this paper, we extend the concept of kings and serfs in tournaments to that of weak kings and weak serfs in oriented graphs. We obtain various results on the existence of weak k…

math.CO2006★ 2 cited

Signed degree sets in signed bipartite graphs

S. Pirzada, T. A. Naikoo, F. A. Dar

A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of posi…

Graphs with {P3​,P4​,P5​}-factors in terms of size and spectral radius

On the spectral redundancy of pineapple graphs

On maximum spectral radius of {H(3,3), H(4,3)}-free graphs

Direct sum graph of the subspaces of a finite dimensional vector space over finite fields

On the Estrada index of unicyclic and bicyclic signed graphs

Spectra of s-neighbourhood corona of two signed graphs

On adjacency and Laplacian cospectral non-isomorphic signed graphs

On Zagreb index, signless Laplacian eigenvalues and signless Laplacian energy of a graph

On graphs with distance Laplacian eigenvalues of multiplicity n−4

On distance Laplacian energy in terms of graph invariants

On the eigenvalues of signed complete bipartite graphs

On a conjecture of Laplacian energy of trees

On normalized Laplacian eigenvalues of power graphs associated to finite cyclic groups

Sphere of Influence Dimension Conjecture 'Almost Proved'

On α-adjacency energy of graphs and Zagreb index

On spectral spread of generalized distance matrix of a graph

Mixing Time of Markov chain of the Knapsack Problem

Spectra and energy of bipartite signed digraphs

On the construction of l-equienergetic graphs

Energy, Laplacian energy of double graphs and new families of equienergetic graphs

Energy of signed digraphs

Imbalances in directed multigraphs

Kings and serfs in oriented graphs

Signed degree sets in signed bipartite graphs

Graphs with ${P_{3}, P_{4}, P_{5}}$ -factors in terms of size and spectral radius

On maximum spectral radius of ${H (3, 3), H (4, 3)}$ -free graphs

On graphs with distance Laplacian eigenvalues of multiplicity $n - 4$

On $α$ -adjacency energy of graphs and Zagreb index