Publications and Work in progress. 

John Caughman, 2006

For a summary of research interests, please refer to my curriculum vitae

  1. Pyramidal one-factorizations and multicolored spanning tree decompositions of K_2n (with J. Krussel),

In preparation.

  1. The Classification of Distance-Regular Graphs that Support a Spin Model,

In preparation.

  1. Kernels of Directed Graph Laplacians (with J. J. P. Veerman),

Electronic Journal of Combinatorics, Vol. 13 (2006), no. 1, Research Papers #39, 8 pages.

  1. Parameter Constraints for a Distance-Regular Graphs that Support a Spin Model (with N. Wolff),

Proceedings of Com2MaC Workshop on Distance-Regular Graphs and Finite Geometry, Pusan, Korea, 2004. pp.125-132.

  1. Lattice Chains and Delannoy Numbers (with C. R. Haithcock and J. J. P. Veerman),

Submitted (2005).

  1. Flocks and Formations (with G. Lafferriere, J. J. P. Veerman, and A. Williams),

Journal of Statistical Physics, Vol. 121 (2005), no. 5/6, pp. 901-936.

  1. Decentralized control of vehicle formations (with G. Lafferriere, J. J. P. Veerman, and A. Williams),

Systems and Control Letters, Vol. 54 (2005), pp. 899-910.

  1.  The Last Subconstituent of the Hemmeter Graph (with E. J. Hart and J. Ma),

Discrete Mathematics, to appear (2005).

  1. The Terwilliger Algebra of an Almost-Bipartite P- and Q-polynomial Association Scheme (with M. Maclean and P. Terwilliger),

Discrete Mathematics, Vol. 292 (2005), no. 1, pp. 17-44.

  1. The Terwilliger Algebra of a Distance-Regular Graph That Supports a Spin Model (with N. Wolff),

Journal of Algebraic Combinatorics, Vol. 21 (2005) no. 3, pp. 289-310.

  1. Graph Theoretic Methods in the Stability of Vehicle Formations (with G. Lafferriere, and A. Williams),

ACC2004, Proceedings of the American Control Conference, pp. 3724-3729 (2004).

  1. Bipartite Q-polynomial Distance-regular Graphs,

Graphs and Combinatorics, Vol. 20 (2004), no. 1, pp. 47-57.

  1. The Last Subconstituent of a Bipartite P- and Q-polynomial Association Scheme,

European Journal of Combinatorics, Vol. 24 (2003), no. 5, pp.459-470.

  1. The Parameters of Bipartite Q-polynomial Distance-regular Graphs,

Journal of Algebraic Combinatorics, Vol. 15 (2002) no. 3, pp.223-229.

  1. The Multiplicities of a Dual-thin Q-polynomial Association Scheme (with B. E. Sagan),

Electronic Journal of Combinatorics, Vol. 8 (2001), no. 1, Notes #4, 5 pages.

  1. Bipartite Q-polynomial Quotients of Antipodal Distance-regular Graphs,

Journal of Combinatorial Theory, Series B, Vol. 76 (1999), pp. 291-296.

  1. The Terwilliger Algebras of Bipartite P- and Q-polynomial Association Schemes,

Discrete Mathematics, Vol. 196 (1999), pp. 65-95.

  1. Spectra of Bipartite P- and Q-polynomial Association Schemes,

Graphs and Combinatorics, Vol. 14 (1998), pp. 321-343.

  1. The Terwilliger algebra for bipartite P- and Q-polynomial association schemes (extended abstract) ,

Surikaisekikenkyusho Kokyuroku, Group Theory and Combinatorial Mathematics (Japanese), No. 991 (1997), pp.108-109.

  1. Intersection Numbers Of Bipartite Distance-Regular Graphs,

Discrete Mathematics, Vol. 163, Issue 1-3 (1997), pp. 235-241. 

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