Publications

Rich mathematical structures arise when algebraic topology meets graph theory, in the framework of discrete cubical homology of graphs. Unlike the conventional approach that models graphs as 1-dimensional simplicial complexes, discrete cubical homology permits the study of higher-dimensional analogues of spheres within a purely discrete setting. Despite the discrete nature of graphs, the computation of these homology groups—even for graphs of modest size—poses significant theoretical as well as algorithmic challenges. My research investigates the computational and combinatorial properties of discrete cubical homology for graphs.

Peer-reviewed publications

Triangular singular cubes in discrete cubical homology
Samira Sahar Jamil and Syed Hadi Ali Zaidi
(in preparation)
On the vanishing of codegree-1 homology cycles in quasimonophobic graphs
Samira Sahar Jamil
(in preparation)
A cubical approach to homology theories for hypergraphs
Syed Hadi Ali Zaidi and Samira Sahar Jamil
Preprint, arXiv, 2026
Monophobic neighborhoods of cubes
Curtis Greene and Samira Sahar Jamil
Preprint, arXiv, 2026
Quasimonophobic graphs and degree spectral sequences in discrete cubical homology
Samira Sahar Jamil and Mark Behrens
To appear in Homology, Homotopy and Applications
Preprint, arXiv, 2026
Computability of digital cubical singular homology of c_1-digital images
Samira Sahar Jamil, P. Christopher Staecker, and Danish Ali
Preprint, arXiv, 2022
Digital Hurewicz theorem and digital homology theory
Samira Sahar Jamil and Danish Ali
Published in Turkish Journal of Mathematics, 2020
Preprint, arXiv.

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