My research is currently supported by an NSF grant DMS-1600768 and has been supported in the past by grants from NSA, Simons Foundation, IdEx Bordeaux and NSERC.

Research Papers

- A spectral version of the Moore problem for bipartite regular graphs submitted, with Jack Koolen and Hiroshi Nozaki.
- Spectral characterization of the complete graph removing a path of small length submitted, with Lihuan Mao and Wei Wang.
- Spectral and combinatorial properties of some algebraically defined graphs submitted, with Felix Lazebnik and Shuying Sun.
- The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters Journal of Combinatorial Theory, Series B, to appear, with Andries Brouwer, Ferdinand Ihringer and Matt McGinnis.
- Distributed calculation of edge-disjoint spanning trees for robustifying distributed algorithms against man-in-the middle attacks IEEE

Transactions on Control of Network Systems, to appear, with Gabriele Oliva and Christoforos N. Hadjicostis. - 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 Applied 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.
- A first course in graph theory and combinatorics, Hindustan Book Agency (2009), +170pp book, with Ram Murty.
- 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).