Submitted Articles:

Brian Kronenthal, Felix Lazebnik, Jason Williford, “On the uniqueness of some girth eight algebraically defined graphs, part II”, submitted to Discrete Applied Mathematics.

J. Verstraete, J. Williford, “Graphs without theta subgraphs”, submitted to Journal of Combinatorial Theory, Series B.

            Refereed Publications:

A. Abiad, B. Brimkov, A. Erey, L. Leshock, X. Martinex-Rivera, S. O, Sung-Yell Song, Jason Williford, “On the Wiener Index, distance cospectrality and transmission regular graphs”, accepted to Discrete Applied Mathematics.

E. Moorhouse, S. Sun, J. Williford, “The eigenvalues of the graphs D(4,q)”, accepted to Journal of Combinatorial Theory, Series B.

E. Moorhouse, J. Williford, “Double covers of symplectic dual polar space graphs”, Discrete Math. 339 (2016).

S. Hobart, J. Williford, “New feasibility conditions for directed strongly regular graphs”, Electronic Journal of Combinatorics 24 (2017).

S. Hobart, J. Williford, “The Absolute Bound for Coherent Configurations”, Linear Algebra and its Applications, (DOI) 10.1016/j.laa.2013.10.045.

  1. S.Hobart, J. Williford, “Tightness in the Semidefinite Bound for Coherent Configurations”, Journal of Algebraic Combinatorics, (DOI) 10.1007/s10801-013-0459-4

            F. Firke, P. Kosek, E. Nash, J. Williford, 2012, “Extremal Graphs Without 4-Cycles”,

Journal of Combinatorial Theory, Series B 103 (2013), pp. 327-336.

  1. S.A. Hobart, J. Williford,  “The independence number for polarity graphs of even order planes”, J. Algebraic Combin. 38 (2013), 57-64.

T. A.Terlep, J. Williford, “Graphs from Generalized Kac-Moody Algebras”, Siam Journal on Discrete Math. 26, no. 3 (2012), 1112-1120.

T. Penttila, J. Williford,  “New examples of Q-polynomial Association Schemes”, Journal of Combinatorial Theory Series A 118, no. 2 (2011), 502—509.

W.J. Martin, J. Williford, “There are finitely many Q-polynomial association schemes of given first multiplicity at least three,” European Journal of Combinatorics 30 (2009), 698—704.

E. Moorhouse and J. Williford, “Embedding Finite Partial Linear Spaces in Finite Translation Nets,” Journal of Geometry 91 (2008), 73—83.

V. Dmytrenko, F. Lazebnik and J. Williford,  “On Monomial Graphs of Girth Eight,” Finite Fields and Their Applications 13 (2007), 828—842.

W.J. Martin, M. Muzychuk and J. Williford, “Imprimitive Cometric Association Schemes: Constructions and Analysis, Journal of Algebraic Combinatorics 25 (2007), 399—415.

D. Mubayi and J. Williford,  “On the Independence Number of the Erdős-Rényi and Projective Norm Graphs and a Related Hypergraph,” Journal of Graph Theory 56 (2007), 113—127.

Non-Refereed Proceedings/Transactions:

W.J. Martin, M. Muzychuk and J. Williford, “Some new constructions of imprimitive cometric association schemes,” Proceedings of Algebraic Combinatorics, an international conference in honour of Eiichi Bannai's 60th birthday (edited by A. Munemasa), Sendai International Center, 2006.

My mathematical interests center around the interplay between algebra, finite geometry and combinatorics. Association schemes and coherent configurations are generalizations of permutation groups that provide a framework in which this interplay is quite rich. Recently, I have focused on generalizing the necessary conditions for existence and subset bounds of association schemes to coherent configurations. I also study extremal problems in graph theory that can be approached using constructions from finite fields and geometries.