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Here is a list of my publications:

 

A Nordhaus-Gaddum type problem for the normalized Laplacian spectrum and graph Cheeger constant (with Nolan Faught and Adam Knudson). Submitted, pre-print: https://arxiv.org/abs/2304.01979

 

Bordering of symmetric matrices and an application to the minimum number of distinct eigenvalues for the join of graphs (with Adia Abiad, Shaun M. Fallat, Rupert H. Levene, Polona Oblak, Helena Smigoc, Michael Tait, and Kevin Vander Meulen). Submitted, pre-print: https://arxiv.org/abs/2303.07949

 

 Isospectral reductions and quantum walks on graphs (with John Tolbert). Submitted, pre-print: https://arxiv.org/abs/2212.00172

 

Effects of Backtracking on PageRank (with Cory Glover, Tyler Jones, and Alice Oveson).  Submitted, pre-print: https://arxiv.org/abs/2211.13353

 

 Unicyclic graphs and the inertia of the distance squared matrix (with Christian Howell, Kellon Sandall, and John Sinkovic). Submitted, pre-print: https://arxiv.org/abs/2211.13341

 

 Kemeny's constant for non-backtracking random walks (with Jane Breen, Nolan Faught, Cory Glover, Adam Knudson, and Alice Oveson).  Random Structures and Algorithms, (2023) 1-21. https://doi.org/10.1002/rsa.21144

 

 On the Laplacian spread of digraphs (with Wayne Barrett, Thomas R. Cameron, Emily Evans, and H. Tracy Hall).  Linear Algebra and its Applications, 664 (2023) 126-146. https://doi.org/10.1016/j.laa.2023.01.016

 

 Fundamentals of fractional revival in graphs (with Ada Chan, Gabriel Coutinho, Whitney Drazen, Or Eisenberg, Chris Godsil, Gabor Lippner, Christino Tamon, and Hanmeng Zhan).  Linear Algebra and its Applications, 655 (2022) 129-158. https://doi.org/10.1016/j.laa.2022.09.010

 

 New conjectures on algebraic connectivity and the Laplacian spread of graphs (with Wayne Barrett, Emily Evans, and H. Tracy Hall).   Linear Algebra and its Applications, 648 (2022) 104-132. https://doi.org/10.1016/j.laa.2022.04.021

 

 SpectralFly: Ramanujan graphs as flexible and efficient interconnection networks (with Stephen Young, Sinan Aksoy, Jesun Firoz, Roberto Gioiosa, Tobias Hagge, Juan Escobedo, and Mark Raugas).  2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS), (2022), 1040-1050. https://doi.org/10.1109/IPDPS53621.2022.00105

 

 A 1-Separation Formula for the Graph Kemeny Constant and Braess Edges (with Nolan Faught and Adam Knudson).  Journal of Mathematical Chemistry, 60 (2022) no. 1, 49-69. https://doi.org/10.1007/s10910-021-01294-8

 

  A homology vanishing theorem for graphs with positive curvature (with Florentin M\"unch and Shing-Tung Yau).   Communications in Analysis and Geometry, 29 (2021) no. 6, 1449-1473. https://dx.doi.org/10.4310/CAG.2021.v29.n6.a5 (pre-print: https://arxiv.org/abs/1710.01264 Note: title of arXiv version: Relationships between cycle spaces, gain graphs, coverings, path homology, and graph curvature).

 

 Pretty good quantum fractional revival in paths and cycles (with Ada Chan, Whitney Drazen, Or Eisenberg, and Gabor Lippner).  Algebraic Combinatorics, 4 (2021) no. 6, 989-1004. https://doi.org/10.5802/alco.189

 

 Spectral Threshold for Extremal Cyclic Edge-Connectivity (with Sinan Aksoy and Stephen J. Young).  Graphs and Combinatorics, 37 (2021), no. 6, 2079-2093. https://doi.org/10.1007/s00373-021-02333-6

 

 Some spectral properties of the non-backtracking matrix of a graph (with Cory Glover).  Linear Algebra and its Applications, 618 (2021), 37-57. https://doi.org/10.1016/j.laa.2021.01.022

 

 Resistance distance, Kirchhoff index, and Kemeny's constant in flower graphs (with Nolan Faught and Adam Knudson).  MATCH Communications in Mathematical and in Computer Chemistry, 86 (2021), no. 2, 405-427. https://match.pmf.kg.ac.rs/electronic_versions/Match86/n2/match86n2_405-427.pdf

 

 Large scale Ricci curvature on graphs (with Gabor Lippner and Florentin Munch).  Calculus of Variations and Partial Differential Equations, 59 (2020) no. 5, 1-17. https://doi.org/10.1007/s00526-020-01829-y

 

 Characterizing cospectral vertices via isospectral reductions (with John Sinkovic, Dallas Smith, and Benjamin Webb).  Linear Algebra and its Applications, 594 (2020), 226-248. https://doi.org/10.1016/j.laa.2020.02.020

 

 Spanning 2-forests and resistance distance in 2-connected graphs (with Wayne Barrett, Emily J. Evans, Amanda E. Francis, and John Sinkovic).  Discrete Applied Mathematics, 284 (2020), 341-352. https://doi.org/10.1016/j.dam.2020.03.061

 

 Perfect state transfer on strongly regular graphs with an edge perturbation (with Chris Godsil, Krystal Guo, Gabor Lippner, and Florentin Munch).   Journal of Combinatorial Theory, Series A, 172 (2020), 105181.  https://doi.org/10.1016/j.jcta.2019.105181

       

 Pretty good quantum state transfer in asymmetric graphs via potential (with Or Eisenberg and Gabor Lippner).  Discrete Mathematics, 342 (2019), no. 10, 2821-2833. https://doi.org/10.1016/j.disc.2018.10.037

 

 A non-backtracking P\'olya's theorem.  Journal of Combinatorics, 9 (2018), no. 2, 327-343. https://doi.org/10.4310/JOC.2018.v9.n2.a6

 

 Pretty good quantum state transfer in symmetric spin networks via magnetic field (with Gabor Lippner and Shing-Tung Yau).  Quantum Information Processing, 16 (2017), no. 210, 1-23.  https://doi.org/10.1007/s11128-017-1658-z

 

 Perfect state transfer on graphs with a potential (with Gabor Lippner and Shing-Tung Yau).  Quantum Information and Computing, 17 (2017), no. 3, 303-327. https://doi.org/10.26421/QIC17.3-4-7

 

 Strong embeddings and 2-isomorphism (with Rani Hod, An Huang, and Shing-Tung Yau).  Notices of the International Congress of Chinese Mathematicians, 4 (2016), no. 2, 5-13. https://dx.doi.org/10.4310/ICCM.2016.v4.n2.a3

 

 Non-backtracking random walks and a weighted Ihara's theorem.  Open Journal of Discrete Mathematics, 6 (2016), no. 4, 207-226. https://doi.org/10.4236/ojdm.2016.64018

 

 A local clustering algorithm for connection graphs (with Fan Chung).   Journal of Internet Mathematics, 11 (2015), 333-351. https://doi.org/10.1080/15427951.2014.968295

 

 Ranking and sparsifying a connection graph (with Fan Chung and Wenbo Zhao).  Journal of Internet Mathematics, 10 (2014), 87-115. https://doi.org/10.1080/15427951.2013.800005

 

 Decompositions of minimum rank matrices (with Wayne Barrett, Nicole Malloy, Curtis Nelson, William Sexton, and John Sinkovic).   Linear Algebra and its Applications, 438 (2013), no. 10, 3913-3948. https://doi.org/10.1016/j.laa.2011.12.036

 

 Minimum rank of outerplanar graphs (with John Sinkovic).   Linear Algebra and its Applications, 436 (2012), no. 9, 3701-3720. https://doi.org/10.1016/j.laa.2012.01.008

 

 The inverse eigenvalue and inertia problems for minimum rank two graphs (with Wayne Barrett, Seth Gibelyou, Nicole Malloy, Curtis Nelson, and John Sinkovic).   Electronic Journal of Linear Algebra, 22 (2011), 389-418. https://doi.org/10.13001/1081-3810.1445