My research interests mainly lie in Combinatorics and Graph Theory, more specifically spectral and extremal graph theory. My works develop a structural approach to look at a graph and study its properties using tools from various areas of mathematics. Extremal graph theory is one of the most interesting fields in modern Graph theory and has risen in popularity over the course of the last few decades. The field of study intrigues me since I love to see how the change in geometrical structures plays a role in the arguments to attain the extremal graphs. Presently, I am exploring area of Graph Algorithm where my aim is to prove existence of faster algorithms for graph clustering and sparsification problems.
People interested in collaborating on related things can always contact me by dropping an email. I will be glad to reply. I am also open to learn new topics in Graph theory and related fields.
I have worked on a few problems related to:
A_{alpha} matrix of graphs.
Distance Matrix of certain classes of graphs.
Extremal graphs with fixed graph parameters like independence number and dissociation number.
Extremal Sombor Index of different graph classes with fixed parameters.
Graph Algorithms.
Graph Clustering and Sparsification.
Squared Distance Matrix.
Wiener Index and Eccentricity of a graph.
Zero Forcing Number of a graph.
Accepted/Published Papers:
J. Das, On the spectral radius of clique trees with a given zero forcing number, Computational and Applied Mathematics Vol: 44, 315, 2025. arXiv:2308.02975.
J. Das, S. De and H. Sun, Online Sparsification of Bipartite-Like Clusters in Graphs, International Conference on Machine Learning ICML 2025 (Accepted).
J. Das and I. Mahato, On the maximum $A_{\alpha}$-spectral radius of unicyclic and bicyclic graphs with a fixed girth or fixed number of pendant vertices, Computational and Applied Mathematics Vol: 43, 347, 2024. arXiv:2311.13364.
J. Das and S. Mohanty. Inverse of the Squared Distance Matrix of a Complete Multipartite Graph, Electronic Journal of Linear Algebra Vol: 40, 475-490, 2024. arXiv:2311.01069.
J. Das and S. Mohanty. Maximization of the spectral radius of block graphs with a given dissociation number, Applied Mathematics and Computation Vol: 465, 128424, 2024. arXiv:2301.12790.
J. Das and S. Mohanty. On Squared Distance Matrix of Complete Multipartite Graphs, Indian Journal of Pure and Applied Mathematics, Vol: 55, 517–537, 2023. arXiv:2012.04341.
D. Bhattacharya and J. Das. A remark on nefness of divisors on surfaces of general type. Studia Scientiarum Mathematicarum Hungarica: Combinatorics, Geometry and Topology, Vol: 59, 3-4, 2022.
J. Das and R. Jana. Proof of a Conjecture on Wiener Index and Eccentricity of a graph due to edge contraction. Discrete Applied Mathematics Vol: 307, 19-21, 2022. arXiv:2104.02930.
J. Das and S. Mohanty. Distance matrix of weighted cactoid-type digraphs, Linear and Multilinear Algebra, Vol: 70, 20, 5392–5422, 2021. arXiv:2001.11262.
J. Das and S. Mohanty. On the spectral radius of bi-block graphs with given independence number $\alpha$, Applied Mathematics and Computation, Vol: 402, 125912, 2021. arXiv:2004.04488.
J. Das and S. Mohanty. Distance matrix of multi-block graphs: determinant and inverse. Linear and Multilinear Algebra, Vol: 70, 19, 3994–4022, 2020. arXiv:1910.01367.
J. Das, S. Jayaraman and S. Mohanty. Distance matrix of a class of completely positive graphs: determinant and inverse. Special Matrices Vol: 8:160-171, 2020. arXiv:1906.04636.
Preprints/Submitted Papers:
J. Das, On extremal Sombor index of trees with a given independence number $\alpha$, preprint. arXiv:2212.10045.
J. Das and Y.K. Prajapaty. On the Sombor Index of Unicyclic graphs with a fixed number of pendant vertices, preprint. arXiv:2212.07732.
Last Updated: June 4, 2025.