Tahir Shamsher

activity

20212026

collaborators

5 papers

math.CO2026

A maximum matching based refinement of Brouwers conjecture

Tahir Shamsher

Let $G$ be a simple graph on $n$ vertices and $e (G)$ edges. Let $μ_{1} \geq \dots \geq μ_{n - 1} \geq μ_{n} = 0$ be the Laplacian eigenvalues of $G$ . For $k = 1, \dots, n$ , let $S_k(G)=\sum_…

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.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…