M. Bhat

activity

20132024

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7 papers · 1 filter

math.CO2024

Variation in $α$ trace norm of a digraph by deletion of a vertex or an arc and its applications

Mushtaq A. Bhat, Peer Abdul Manan

Let $D$ be a digraph of order $n$ with adjacency matrix $A (D)$ . For $α \in [0, 1)$ , the $A_{α}$ matrix of $D$ is defined as $A_{α} (D) = α Δ^{+} (D) + (1 - α) A (D)$ , where $Δ^{+}(D)=\mbox{diag}~(d_…

math.CO2024

Bounds for the trace norm of $A_{α}$ matrix of digraphs

Mushtaq A. Bhat, Peer Abdul Manan

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.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.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.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

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…

Variation in α trace norm of a digraph by deletion of a vertex or an arc and its applications

Bounds for the trace norm of Aα​ matrix of digraphs