**What work I have done I have done because it has been play. If it had been work I shouldn’t have done it.
**

Books

- 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
- 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

- Clique complexes of strongly regular graphs and their eigenvalues, in preparation, with Krystal Guo, Chunxu Ji and Mutasim Mim.
- The spectral even cycle problem, Combinatorial Theory, in revision, with Dheer Noal and Mike Tait.
- A spectral Erdős-Sós theorem, SIAM Journal of Discrete Mathematics (2023), with Dheer Noal and Mike Tait.
- Graph rigidity properties of Ramanujan graphs, The Electronic Journal of Combinatorics (2023), with Sean Dewar, Georg Grasegger and Xiaofeng Gu.
- The least Euclidean distortion of a distance-regular graph, Discrete Applied Mathematics (2023), with Himanshu Gupta, Ferdinand Ihringer and Hirotake Kurihara.
- 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.
- 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.
- On the spectrum and linear programming bound for hypergraphs, European Journal of Combinatorics, (2022), with Jack Koolen, Masato Mimura, Hiroshi Nozaki and Takayuki Okuda.
- On the eigenvalues of Grassmann graphs, Bilinear forms graphs and Hermitian forms graphs, Graphs and Combinatorics, (2022), with Himanshu Gupta.
- The spectral radius of graphs with no odd wheels, European Journal of Combinatorics, (2022), with Dheer Noal Desai and Michael Tait.
- The chromatic index of strongly regular graphs, Ars Mathematica Contemporanea, (2021), with Krystal Guo and Willem Haemers.
- 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
- 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.
- Addressing Johnson graphs, complete multipartite graphs, odd cycles and random graphs, Experimental Mathematics, (2021), with Noga Alon, Brandon Gilbert, Jack Koolen and Brendan McKay.
- Spectral conditions for graph rigidity in the Euclidean plane, Discrete Mathematics, (2021), with Sean Dewar and Xiaofeng Gu. ICERM talk
- The toughness of Kneser graphs, Discrete Mathematics, (2021), with Davin Park, Anthony Ostuni, Nathan Hayes, Amartya Banerjee, Tanay Wakhare and Wiseley Wong.
- 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.
- 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.
- The spectral radius of graphs with no intersecting triangles, The Electronic Journal of Combinatorics, (2020), with Lihua Feng, Michael Tait and Xiaodong Zhang.
- Eigenvalues of graphs and spectral Moore theorems, RIMS Kôkyûroku, (2020).
- 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.
- A spectral version of the Moore problem for bipartite regular graphs, Algebraic Combinatorics (2019), with Jack Koolen and Hiroshi Nozaki.
- Optimal sampling sets for cographs, IEEE Data Science Workshop 2019 with Dominique Guillot, Alejandro Parada and Gonzalo Arce.
- The second eigenvalue of some normal Cayley graphs of highly transitive groups, The Electronic Journal of Combinatorics (2019), with Xueyi Huang and Qingxiang Huang.
- Spectral characterization of the complete graph removing a path of small length Discrete Applied Mathematics (2019), with Lihuan Mao and Wei Wang.
- 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.
- Spectral and combinatorial properties of some algebraically defined graphs The Electronic Journal of Combinatorics (2018), with Felix Lazebnik and Shuying Sun.
- 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.
- 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.
- 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.
- Max-cut and extendability of matchings in distance-regular graphs European Journal of Combinatorics (2017), with Jack Koolen and Weiqiang Li.
- The graphs with all but two eigenvalues equal to -2 or 0 Designs, Codes and Cryptography (2017), with Willem Haemers and Jason Vermette.
- Addressing graph products and distance-regular graphs Discrete Applied Mathematics (2017), with Randall J. Elzinga, Michelle Markiewitz, Kevin Vander Meulen and Trevor Vanderwoerd.
- Notes on simplicial rook graphs Journal of Algebraic Combinatorics (2016), with Andries Brouwer, Willem Haemers and Jason Vermette.
- 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.
- Spectral bounds for the k-independence number of a graph Linear Algebra and its Applications (2016), with Aida Abiad and Michael Tait.
- Connectivity, toughness, spanning trees of bounded degree and the spectrum of regular graphs Czechoslovak Mathematical Journal (2016), with Xiaofeng Gu.
- The graphs with all but two eigenvalues +1/-1 Journal of Algebraic Combinatorics (2015), with Willem Haemers, Jason Vermette and Wiseley Wong.
- A graph partition problem American Mathematical Monthly (2015), with Peter Cameron.
- Mixing rates of random walks with little backtracking AMS Contemporary Mathematics (2015), with Peng Xu.
- On the spectrum of Wenger graphs Journal of Combinatorial Theory, Series B (2014), with Felix Lazebnik and Weiqiang Li.
- Disconnecting strongly regular graphs European Journal of Combinatorics (2014), with Jack Koolen and Weiqiang Li.
- The extendability of matchings in strongly regular graphs The Electronic Journal of Combinatorics (2014), with Weiqiang Li.
- The spectrum and toughness of regular graphs Discrete Applied Mathematics (2014), with Wiseley Wong.
- On the connectedness of the complement of a ball in a distance-regular graph Journal of Algebraic Combinatorics (2013), with Jack Koolen.
- Variations on a theme of Graham and Pollak Discrete Mathematics (2013), with Michael Tait.
- Ramanujan and expander graphs Chapter in the Handbook of Finite Fields (2013), with Ram Murty.
- 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.
- Covering complete hypergraphs with cuts of minimum total size Graphs and Combinatoris (2012), with Andre Kundgen.
- Edge-disjoint spanning trees and eigenvalues of regular graphs Linear Algebra and its Applications (2012), with Wiseley Wong.
- 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.
- More counterexamples to the Alon-Saks-Seymour and Rank-Coloring conjectures The Electronic Journal of Combinatorics (2011), with Michael Tait.
- Covering complete r-graphs with spanning complete r-partite r-graphs Combinatorics, Probability and Computing (2011), with Craig Timmons, Andre Kundgen and Vladislav Vysotsky.
- Some applications of eigenvalues of graphs, Chapter 14 in Structural Analysis of Complex Networks, Birkhauser (2011), Editor: Matthias Dehmer.
- Edge-connectivity, eigenvalues and matchings in regular graphs SIAM Journal of Discrete Mathematics (2010), with Suil O.
- 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.
- A necessary and sufficient eigenvector condition for a graph to be bipartite Electronic Journal of Linear Algebra (2010).
- Eigenvalues and edge-connectivity of regular graphs Linear Algebra and its Applications (2010).
- 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.
- On decompositions of complete hypergraphs Journal of Combinatorial Theory, Series A (2009), with Andre Kundgen and Jacques Verstraete.
- Matchings in regular graphs from eigenvalues Journal of Combinatorial Theory, Series B (2009), with David Gregory and Willem Haemers.
- The minimum degree distance of graphs of given order and size Discrete Applied Mathematics (2008), with Orest Bucicovschi.
- Expander graphs and gaps between the primes Forum Mathematicum (2008), with Ram Murty.
- The spectral radius and the maximum degree of irregular graphs The Electronic Journal of Combinatorics (2007).
- Principal eigenvectors of irregular graphs Electronic Journal of Linear Algebra (2007), with David Gregory.
- Extremal eigenvalues of nonregular graphs Journal of Combinatorial Theory, Series B (2007), with David Gregory and Vladimir Nikiforov.
- Spectral densest subgraph and independence number of a graph Journal of Universal Computer Sciences (2007), with Reid Andersen.
- Eigenvalues of graphs and a simple proof of a theorem of Greenberg Linear Algebra and its Applications (2006).
- Sums of powers of the degrees of a graph Discrete Mathematics (2006).
- Closed walks and eigenvalues of Abelian Cayley graphs Comptes Rendus (2006).
- On the extreme eigenvalues of regular graphs Journal of Combinatorial Theory, Series B (2006).
- Eigenvalues, expanders and gaps between primes Ph.D Thesis (2005).
- Perfect matchings, eigenvalues and expansion Comptes Rendus Mathématiques de l’Académie des Sciences. La Société Royale du Canada (2005).
- Bounds on the Turan density of PG(3,2) The Electronic Journal of Combinatorics (2004).
- The NP-completeness of some edge partitioning problems M.Sc. Thesis (2002).

My research is currently supported by the NSF grant CIF-1815922 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.