We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.

Books

  1. A Bridge to Advanced Mathematics: From Natural to Complex Numbers, with Werner Linde, 525 pages, January 2023, published by American Math Society in the AMSTEXT series MAA review
  2. A First Course in Graph Theory and Combinatorics, HBA Trim Series with Ram Murty Errata to 1st edition., HBA Trim Series 2nd edition (2021), published by Springer in 2022.

Research Papers

  1. Clique complexes of strongly regular graphs and their eigenvalues, in preparation, with Krystal Guo, Chunxu Ji and Mutasim Mim.
  2. On the minimum spectral radius of connected graphs of given order and size, Special Matrices, (2024) Special Issue in honor of Prof. Nair Maria Abreu,  with Vishal Gupta and Celso Marques.
  3. The spectral even cycle problem, Combinatorial Theory, (2024), with Dheer Noal and Mike Tait.
  4. A spectral Erdős-Sós theorem, SIAM Journal of Discrete Mathematics (2023), with Dheer Noal and Mike Tait.
  5. Graph rigidity properties of Ramanujan graphs, The Electronic Journal of Combinatorics (2023), with Sean Dewar, Georg Grasegger and Xiaofeng Gu.
  6. The least Euclidean distortion of a distance-regular graph, Discrete Applied Mathematics (2023), with Himanshu Gupta, Ferdinand Ihringer and Hirotake Kurihara.
  7. A lower bound on the smallest eigenvalue of a graph and an application to the associahedron graph, Bulletin of the Romanian Mathematical Society (2022), with Vishal Gupta.
  8. Extremal graphs for a spectral inequality on edge-disjoint spanning trees, The Electronic Journal of Combinatorics, (2022), with Anthony Ostuni, Davin Park, Sriya Potluri, Tanay Wakhare and Wiseley Wong.
  9. On the spectrum and linear programming bound for hypergraphs, European Journal of Combinatorics, (2022), with Jack Koolen, Masato Mimura, Hiroshi Nozaki and Takayuki Okuda.
  10. On the eigenvalues of Grassmann graphs, Bilinear forms graphs and Hermitian forms graphs, Graphs and Combinatorics, (2022), with Himanshu Gupta.
  11. The spectral radius of graphs with no odd wheels, European Journal of Combinatorics, (2022), with Dheer Noal Desai and Michael Tait.
  12. The chromatic index of strongly regular graphs, Ars Mathematica Contemporanea, (2021), with Krystal Guo and Willem Haemers.
  13. On the flip graphs on perfect matchings of complete graphs and signed reversal graphs, Australasian Journal of Combinatorics, (2021), with Gordon Royle and Zhao Kuang Tan. Waterloo talk July 2020
  14. Identifying Brain Regions Supporting Amygdala Functionality: A Complex Anatomical Network Perspective, Neuroimage, (2021), with Melanie A. Matyi, Marie T. Banich and Jeff Spielberg, Biological Psychiatry, poster.
  15. Addressing Johnson graphs, complete multipartite graphs, odd cycles and random graphs, Experimental Mathematics, (2021), with Noga Alon, Brandon Gilbert, Jack Koolen and Brendan McKay.
  16. Spectral conditions for graph rigidity in the Euclidean plane, Discrete Mathematics, (2021), with Sean Dewar and Xiaofeng Gu. ICERM talk
  17. The toughness of Kneser graphs, Discrete Mathematics, (2021), with Davin Park, Anthony Ostuni, Nathan Hayes, Amartya Banerjee, Tanay Wakhare and Wiseley Wong.
  18. On a question of Haemers regarding vectors in the nullspace of Seidel matrices, Linear Algebra and its Applications, (2021), with Saieed Akbari, Samira Goudarzi, Aidin Niaparast and Artin Tajdini.
  19. Connectivity concerning the last two subconstituents of a Q-polynomial distance-regular graph, Journal of Combinatorial Theory, Series A, (2021), with Jack Koolen and Paul Terwilliger.
  20. The spectral radius of graphs with no intersecting triangles, The Electronic Journal of Combinatorics, (2020), with Lihua Feng, Michael Tait and Xiaodong Zhang.
  21. Eigenvalues of graphs and spectral Moore theorems, RIMS Kôkyûroku, (2020).
  22. Some observations on the smallest eigenvalue of a graph, Discussiones Mathematicae Graph Theory, Special issue in honor of Slobodan K. Simic, 2020, with David Gregory and Randy Elzinga.
  23. A spectral version of the Moore problem for bipartite regular graphs, Algebraic Combinatorics (2019), with Jack Koolen and Hiroshi Nozaki.
  24. Optimal sampling sets for cographs, IEEE Data Science Workshop 2019 with Dominique Guillot, Alejandro Parada and Gonzalo Arce.
  25. The second eigenvalue of some normal Cayley graphs of highly transitive groups, The Electronic Journal of Combinatorics (2019), with Xueyi Huang and Qingxiang Huang.
  26. Spectral characterization of the complete graph removing a path of small length Discrete Applied Mathematics (2019), with Lihuan Mao and Wei Wang.
  27. Open problems in the spectral theory of signed graphs, The Art of Discrete and Applied Mathematics, (2018) with Francesco Belardo, Jack Koolen and Jianfeng Wang.
  28. Spectral and combinatorial properties of some algebraically defined graphs The Electronic Journal of Combinatorics (2018), with Felix Lazebnik and Shuying Sun.
  29. Distributed calculation of edge-disjoint spanning trees for robustifying distributed algorithms against man-in-the middle attacks IEEE Transactions on Control of Network Systems (2018), with Gabriele Oliva and Christoforos N. Hadjicostis.
  30. The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters Journal of Combinatorial Theory, Series B (2018), with Andries Brouwer, Ferdinand Ihringer and Matt McGinnis.
  31. Cospectral mates for the union of some classes in the Johnson scheme Linear Algebra and its Applications (2018), with Willem Haemers, Travis Johnston and Matt McGinnis.
  32. Max-cut and extendability of matchings in distance-regular graphs European Journal of Combinatorics (2017), with Jack Koolen and Weiqiang Li.
  33. The graphs with all but two eigenvalues equal to -2 or 0 Designs, Codes and Cryptography (2017), with Willem Haemers and Jason Vermette.
  34. Addressing graph products and distance-regular graphs Discrete Applied Mathematics (2017), with Randall J. Elzinga, Michelle Markiewitz, Kevin Vander Meulen and Trevor Vanderwoerd.
  35. Notes on simplicial rook graphs Journal of Algebraic Combinatorics (2016), with Andries Brouwer, Willem Haemers and Jason Vermette.
  36. Maximizing the order of a regular graph of given valency and second eigenvalue SIAM Journal of Discrete Mathematics (2016), with Jack Koolen, Hiroshi Nozaki and Jason Vermette.
  37. Spectral bounds for the k-independence number of a graph Linear Algebra and its Applications (2016), with Aida Abiad and Michael Tait.
  38. Connectivity, toughness, spanning trees of bounded degree and the spectrum of regular graphs Czechoslovak Mathematical Journal (2016), with Xiaofeng Gu.
  39. The graphs with all but two eigenvalues +1/-1 Journal of Algebraic Combinatorics (2015), with Willem Haemers, Jason Vermette and Wiseley Wong.
  40. A graph partition problem American Mathematical Monthly (2015), with Peter Cameron.
  41. Mixing rates of random walks with little backtracking AMS Contemporary Mathematics (2015), with Peng Xu.
  42. On the spectrum of Wenger graphs Journal of Combinatorial Theory, Series B (2014), with Felix Lazebnik and Weiqiang Li.
  43. Disconnecting strongly regular graphs European Journal of Combinatorics (2014), with Jack Koolen and Weiqiang Li.
  44. The extendability of matchings in strongly regular graphs The Electronic Journal of Combinatorics (2014), with Weiqiang Li.
  45. The spectrum and toughness of regular graphs Discrete Applied Mathematics (2014), with Wiseley Wong.
  46. On the connectedness of the complement of a ball in a distance-regular graph Journal of Algebraic Combinatorics (2013), with Jack Koolen.
  47. Variations on a theme of Graham and Pollak Discrete Mathematics (2013), with Michael Tait.
  48. Ramanujan and expander graphs Chapter in the Handbook of Finite Fields (2013), with Ram Murty.
  49. On a conjecture of Brouwer involving the connectivity of strongly regular graphs Journal of Combinatorial Theory, Series A (2012), with Jack Koolen and Kijung Kim.
  50. Covering complete hypergraphs with cuts of minimum total size Graphs and Combinatoris (2012), with Andre Kundgen.
  51. Edge-disjoint spanning trees and eigenvalues of regular graphs Linear Algebra and its Applications (2012), with Wiseley Wong.
  52. Skew-adjacency matrices of graphs Linear Algebra and its Applications (2012), with Michael Cavers, Shaun Fallat, David Gregory, Willem Haemers, Steve Kirkland, Judi McDonald and Michael Tsatsomeros.
  53. More counterexamples to the Alon-Saks-Seymour and Rank-Coloring conjectures The Electronic Journal of Combinatorics (2011), with Michael Tait.
  54. Covering complete r-graphs with spanning complete r-partite r-graphs Combinatorics, Probability and Computing (2011), with Craig Timmons, Andre Kundgen and Vladislav Vysotsky.
  55. Some applications of eigenvalues of graphs, Chapter 14 in Structural Analysis of Complex Networks, Birkhauser (2011), Editor: Matthias Dehmer.
  56. Edge-connectivity, eigenvalues and matchings in regular graphs SIAM Journal of Discrete Mathematics (2010), with Suil O.
  57. A lower bound for the spectral radius of graphs with fixed diameter European Journal of Combinatorics (2010), with Edwin van Dam, Jack Koolen and Jae-Ho Lee.
  58. A necessary and sufficient eigenvector condition for a graph to be bipartite Electronic Journal of Linear Algebra (2010).
  59. Eigenvalues and edge-connectivity of regular graphs Linear Algebra and its Applications (2010).
  60. Asymptotic results on the spectral radius and the diameter of graphs Linear Algebra and its Applications (2010), with Edwin van Dam, Jack Koolen and Jae-Ho Lee.
  61. On decompositions of complete hypergraphs Journal of Combinatorial Theory, Series A (2009), with Andre Kundgen and Jacques Verstraete.
  62. Matchings in regular graphs from eigenvalues Journal of Combinatorial Theory, Series B (2009), with David Gregory and Willem Haemers.
  63. The minimum degree distance of graphs of given order and size Discrete Applied Mathematics (2008), with Orest Bucicovschi.
  64. Expander graphs and gaps between the primes Forum Mathematicum (2008), with Ram Murty.
  65. The spectral radius and the maximum degree of irregular graphs The Electronic Journal of Combinatorics (2007).
  66. Principal eigenvectors of irregular graphs Electronic Journal of Linear Algebra (2007), with David Gregory.
  67. Extremal eigenvalues of nonregular graphs Journal of Combinatorial Theory, Series B (2007), with David Gregory and Vladimir Nikiforov.
  68. Spectral densest subgraph and independence number of a graph Journal of Universal Computer Sciences (2007), with Reid Andersen.
  69. Eigenvalues of graphs and a simple proof of a theorem of Greenberg Linear Algebra and its Applications (2006).
  70. Sums of powers of the degrees of a graph Discrete Mathematics (2006).
  71. Closed walks and eigenvalues of Abelian Cayley graphs Comptes Rendus (2006).
  72. On the extreme eigenvalues of regular graphs Journal of Combinatorial Theory, Series B (2006).
  73. Eigenvalues, expanders and gaps between primes Ph.D Thesis (2005).
  74. Perfect matchings, eigenvalues and expansion Comptes Rendus Mathématiques de l’Académie des Sciences. La Société Royale du Canada (2005).
  75. Bounds on the Turan density of PG(3,2) The Electronic Journal of Combinatorics (2004).
  76. The NP-completeness of some edge partitioning problems M.Sc. Thesis (2002).

My research is currently supported by the NSF award DMS-2245556 (Spectral and extremal graph theory, I am co-PI, PI Mike Tait)and has been supported in the past by grants from NSF, JSPS, NSA, Simons Foundation, IdEx Bordeaux and NSERC. My co-authors are from Canada, USA, Bulgaria, Romania, The Netherlands, Serbia, India, Malta, Germany, South Africa, South Korea, Ukraine, Greece, China, Catalunya, Japan, Italy, Cyprus, Colombia, Israel, Australia, Singapore, Iran, England.

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