Samir Shukla - Research

My area of research lies in Applied Topology and Combinatorics. I am interested in the applications of topology in graph theory, combinatorics, and other related fields. The following is the list of my publications and preprints.

Published:

On the matching complexes of categorical product of path graphs (with Raju Kumar Gupta, Sourav Sarkar and Sagar S. Sawant),

Journal of Applied and Computational Topology, 10, (19) 2026, DOI [arXiv]

Shellability of 3-cut complexes of squared cycle graphs (with Pratiksha Chauhan and Kumar Vinayak),

Journal of Homotopy and Related Structures, Volume:20, page 163-1923, 2025, DOI [arXiv]

Čech complexes of hypercube graphs, (with Henry Adams and Anurag Singh),

Homology, Homotopy and Applications , Volume:27, pp 83-105, 2025, DOI [arXiv]

Connectedness of certain graph coloring complexes, (with Nandini Nilakantan),

Topology and its Applications, Volume:354, 108985, 2024, [arXiv]

On Vietoris-Rips complexes (with scale 3) of hypercube graphs,

SIAM Journal on Discrete Mathematics, 37.3, pp. 1472-1495, 2023 [arXiv]

Vertex cut of a graph and topological connectivity of its neighborhood complex, (with Rekha Santhanam)

Discrete Mathematics, 364.8, 113432, 2023 [arXiv]

Neighborhood complexes, homotopy test graphs and an application to coloring of product graphs,

Graphs and Combinatorics, 38.3, 1-14, 2022, [arXiv]

Distance r-domination number and r-independence complexes of graphs, (with Priyavrat Deshpande and Anurag Singh),

European Journal of Combinatorics, 102, 103508, 2022, [arXiv]

Topology of clique complexes of line graphs, (with Shuchita Goyal and Anurag Singh)

The Art of Discrete and Applied Mathematics, 5, no 2, Paper no:2.06, 12 pp, 2022, [arXiv]

Homotopy type of independence complexes of certain families of graphs, (with Shuchita Goyal and Anurag Singh),

Contributions to Discrete Mathematics, 16.3, 74-92, 2021, [arXiv]

Matching complexes of 3 x n grid graphs, (with Shuchita Goyal and Anurag Singh)

The Electronic Journal of Combinatorics, 28, no.4: P4.16, 2021.

(Paper withdrawn by the authors due to an error in the proof of main result)

Spectral gap bounds for the simplicial Laplacian and an application to random complexes, (with D. Yogeshwaran),

Journal of Combinatorial Theory, Series A 169, 105134, 20 pp., 2020 [arXiv]

Homotopy type of the neighborhood complexes of graphs of maximal degree at most 3 and 4-regular circulant graphs,

The Electronic Journal of Combinatorics, 26, no. 2: P2.4, 2019.

Neighborhood complexes of some exponential graphs, (with Nandini Nilakantan),

The Electronic Journal of Combinatorics, 23, no. 2: P2.26, 2016.

Preprints:

Homology of matching complexes of $3\times n$ grid graphs (with Pratiksha Chauhan and Anchal Sharma) [arXiv]
Shellability of 3-cut complexes of powers of cycle graphs (submitted) (with Pratiksha Chauhan) [arXiv]
Total 2-cut complexes of powers of cycle graphs and Cartesian products of certain graphs (submitted) (with Pratiksha Chauhan and Kumar Vinayak) [arXiv]
On the Vietoris-Rips complexes of Integer Lattices (with Raju Kumar Gupta, Sourav Sarkar ) (submitted) [arXiv]
Bounds for the collapsibility number of a simplicial complex and non-cover complexes of hypergraphs, (with Rekha Santhanam and Anurag Singh) (submitted), [arXiv]

Homotopy type of the independence complexes of a family of regular bipartite graphs., (with Nandini Nilakantan), [arXiv]

Collaborators:

Henry Adams (University of Florida)
Priyavrat Deshpande (Chennai Mathematical Institute, Chennai, India)
Shuchita Goyal (BITS Pilani, India)
Raju Kumar Gupta (Slovak Academy of Sciences, Bratislava, Slovakia )
Nandini Nilaknatan (Indian Institute of Technology Kanpur, India)
Rekha Santhanam (Indian Institute of Technology Bombay, India)
Sourav Sarkar (Pusan National University, Busan, South Korea)
Sagar Sawant (Chennai Mathematical Institute, India)
Anurag Singh (Indian Institute of Technology Bhilai, India)
Kumar Vinayak (University of Kentucky, USA)
D. Yogeshwaran (Indian Statistical Institute Bangalore, India )

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