M. Nagar

activity

20172026

most citedLaplacian Immanantal polynomials and the GTS poset on Trees

4 citations · 5 across the 7 of their papers we have counts for

collaborators

7 papers

math.CO2026

On Spectra of $T$ -Gain Digraphs

Shivani Tushar Parab, Tarkeshwar Singh, Mukesh Kumar Nagar

A $\mathbb{T}$-gain digraph is a directed graph with complex unit gains on its arcs, allowing for no restrictions on oppositely directed arcs. This framework unifies various grap…

math.CO2023

The maximum four point condition matrix of a tree

Ali Azimi, Rakesh Jana, Mukesh Kumar Nagar +1

The Four point condition (4PC henceforth) is a well known condition characterising distances in trees $T$ . Let $w, x, y, z$ be four vertices in $T…

math.CO2023

Inequalities among two rowed immanants of the $q$ -Laplacian of Trees and Odd height peaks in generalized Dyck paths

Mukesh Kumar Nagar, Arbind Kumar Lal, Sivaramakrishnan Sivasubramanian

Let $T$ be a tree on $n$ vertices and let $L_{q}^{T}$ be the $q$ -analogue of its Laplacian. For a partition $λ ⊢ n$ , let the normalized immanant of $L_{q}^{T}$ indexed by $λ$ be denote…

math.CO2023

Laplacian Immanantal Polynomials of a Bipartite Graph and Graph Shift Operation

Mukesh Kumar Nagar

Let $G$ be a bipartite graph on $n$ vertices with the Laplacian matrix $L_{G}$ . When $G$ is a tree, inequalities involving coefficients of immanantal polynomials of $L_{G}$ are known a…

math.CO2019

Generalized Matrix polynomials of Tree Laplacians indexed by Symmetric functions and the GTS poset

Mukesh Kumar Nagar, Sivaramakrishnan Sivasubramanian

Let $T$ be a tree on $n$ vertices with $q$ -Laplacian $L_{T}^{q}$ and Laplacian matrix $L_{T}$ . Let $GT S_{n}$ be the generalized tree shift poset on the set of unlabelled trees on $n$ verti…

math.CO2017★ 1 cited

Eigenvalue monotonicity of $q$ -Laplacians of trees along a poset

Mukesh Kumar Nagar

Let $T$ be a tree on $n$ vertices with $q$ -Laplacian $L_{T}^{q}$ . Let $GT S_{n}$ be the generalized tree shift poset on the set of unlabelled trees with $n$ vertices. We prove that fo…

math.CO2017★ 4 cited

Laplacian Immanantal polynomials and the GTS poset on Trees

Mukesh Kumar Nagar, Sivaramakrishnan Sivasubramanian

Let $T$ be a tree on $n$ vertices with Laplacian $L_{T}$ and let $GT S_{n}$ be the generalized tree shift poset on the set of unlabelled trees on $n$ vertices. Inequalities are known fo…

On Spectra of T-Gain Digraphs

The maximum four point condition matrix of a tree

Inequalities among two rowed immanants of the q-Laplacian of Trees and Odd height peaks in generalized Dyck paths

Laplacian Immanantal Polynomials of a Bipartite Graph and Graph Shift Operation

Generalized Matrix polynomials of Tree Laplacians indexed by Symmetric functions and the GTS poset

Eigenvalue monotonicity of q-Laplacians of trees along a poset

Laplacian Immanantal polynomials and the GTS poset on Trees

On Spectra of $T$ -Gain Digraphs

Inequalities among two rowed immanants of the $q$ -Laplacian of Trees and Odd height peaks in generalized Dyck paths

Eigenvalue monotonicity of $q$ -Laplacians of trees along a poset