Research Publications

  1. An Analytic Triangulation of an Arbitrary Analytic Variety, J. MATH. MECH., Vol. 13 (1964), No. 6, pp. 1021-1036, [MR0167989]
  2. An Upper Bound for Ramsey Numbers (with James Yackel), BULL. AMER. MATH. SOC., Vol. 72 (1966), No. 6, pp. 1076-1079, [MR0199120]
  3. Some Graph Theoretic Results Associated with Ramsey’s Theorem (with J. Yackel), J. COMBINATORIAL THEORY, Vol. 4 (1968), No. 2, pp. 125-175, [MR0225685].
  4. ) Remarks on the Parameters of a System of Sets, ANN. N.Y. ACAD. SCIENCE, Vol. 175 (7/3/1970), Article 1, pp. 187-198, [MR0294140]
  5. The Groups of the Generalized Petersen Graphs, (with M.E. Watkins and R. Frucht), PROC. CAMBRIDGE PHIL. SOC., Vol. 70 (September 1971), pp. 211-218, [MR0289365]
  6. A characterization of Symmetric Block Designs, J. COMBINATORIAL THEORY, Vol. 12, No. 2 (March 1972), pp. 304-308, [MR0295929]
  7. Algebra-Structures for General Designs, (with W.B. Jurkat), J. OF ALGEBRA, Vol. 23 (December 1972), No. 3, pp. 574-589, [MR0309767]
  8. The Module Structure of Integral Designs, (with W.B. Jurkat), J. COMB. THEORY, Vol. 15 (July 1973), No. 1, pp. 75-90, [MR0329930]
  9. Boolean Designs and Self-Dual Matroids, LINEAR ALGEBRA AND APPLICATIONS, Vol. 10, (1975), pp. 111-128, [MR9376400]
  10. A Survey of the Maximum Depth Problems for Indecomposable Exact Covers, PROCEEDINGS OF THE INTERNATIONAL COLLOQUIUM OF INFINITE AND FINITE SETS, (held in June 1973 at Kreszthely, Hungary), Springer-Verlag, pp. 731-743, [MR0401516]
  11. On the Foundations of Linear Integer Programming I, MATHEMATICAL PROGRAMMING, Vol. 9, No. 2, October 1975, pp. 207-226, [MR0386673]
  12. Mean Distance in a Graph, (with J.K. Doyle), DISCRETE MATHEMATICS, Vol. 17, No. 2, (Feb. 1977), pp. 147-154, [MR0485476]
  13. Mean Distance in a Directed Graph, (with J.K. Doyle), ENVIRONMENT AND PLANNING B, Vol. 5, No. 1 (June 1978), pp. 19-30.
  14. The Imbedding Index of a Graph, J. COMBINATORIAL THEORY B, Vol. 27, No. 2 (October 1979(, pp. 151-159, [MR0546857]
  15. f-Factors and Related Decompositions of Graphs (with W.B. Jurkat), J. COMBINATORIAL THEORY B, Vol. 28, No. 1 (February 1980), pp. 66-84, [MR0565511]
  16. Mean Distance for Shapes (with J.K. Doyle), J. GRAPH THEORY , Vol. 6, No. 4, (December 1982), pp. 453-478, [MR0679602]
  17. A Characterization of Finite Planar Primitive Graphs (with M. Watkins), SCIENTIA., SER. A: MATHEMATICAL SCIENCES, Vol. 1 (1988), pp. 59-60. [MR2313048]
  18. Rigidity Matroids, SIAM JOURNAL ON DISCRETE MATHEMATICS, Vol. 4, No 3 (August 1991), pp.355-368. [MR1105942]
  19. Abstract rigidity in m-Space, (with B&H. Servatius), CONTEMPORARY MATHEMATICS, Vol. 178 (1994), pp.145-151. [MR1310581]
  20. On the Structure of Locally Finite, Planar, Edge-Transitive Graphs (with M. Watkins) MEMOIRS OF THE AMERICAN MATHEMATICAL, Vol. 126 No. 602 (1997), 87 pages. [MR1361828]
  21. Designing a Mirror that Inverts in a Circle, (with G. Cargo and J. Troutman) THE MATHEMATICAL INTELLIGENCER, Vol.24, No. 1 (2002), pp.4-8.
  22. The (m,k)-patch boundary code problem, MATCH (Communications in Mathematical and in Computer Chemistry) Vol. 48 (2003), pp 189-196. [MR1989001]
  23. A characterization of infinite planar primitive graphs, (with Mark Watkins), J. COMBINATORIAL THEORY B, Vol. 19 No. 1 (2004), pp 87-104. [MR2047533]
  24. Encoding Fullerenes and Geodesic Domes, SIAM. J. DISCRETE MATH, Vol. 17, No. 4 (2004), pp 596-614. [MR2085216]
  25. The Structure of Fullerenes, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 69, AMS, (2005), pp137-166. [MR2193448]
  26. A catalog of fullerenes with 10 or more symmetries, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 69, AMS, (2005), pp167-188. [MR2193449] [A list of corrections has been added at the end of this paper.]
  27. You may rely on the reliability polynomial for much more than you might expect, (with Milton Sobel), COMMUNICATIONS IN STATISTICS – THEORY AND METHODS, Vol. 34, No. 6 (2005), pp 1411-1422. [MR2162099]
  28. The independence number of fullerenes and benzenoids, THE EUROPEAN JOURNAL OF COMBINATORICS, Vol. 27, Issue 6 (2006) pp 850-863. [MR2226422]
  29. Growing fullerenes from seed: growth transformations of fullerene polyhedra, (with G. Brinkmann, D. Franceus and P. Fowler), CHEMICAL PHYSICS LETTERS, 428 (2006) pp386-393.
  30. A note on natural correspondences that satisfy exclusion, SOCIAL CHOICE AND WELFARE, 29 (2007) pp105-106. [MR2318340]
  31. Kekule structures and face independence number of a fullerene, THE EUROPEAN JOURNAL OF COMBINATORICS, Vol. 28, Issue 4 (2007) pp 1115-1130. ;MR2305578]
  32. Numbers of Faces in Disordered Patches, (with Gunnar Brinkmann & Claudia Justus), JOURNAL OF MATHEMATICAL CHEMISTRY, Vol. 45. No. 2 (2009) pp 263-278. [MR2470459]
  33. Highly Symmetric Fullerenes and Nanotubes, (with Yvette Monachino), Symmetry in Nanostructures, a special issue of SYMMETRY: CULTURE AND SCIENCE Vol. 19, Num. 4 (2009) pp 317-340.
  34. Fullerene Patches I, (with Christy Graves), ARS MATHEMATICA COMTEMPORANEA, Vol. 3 (2010) pp109-120. [MR2643922]
  35. When does a curve bound a distorted disk? (with G. Cargo), SIAM JOURNAL OF DISCRETE MATHEMATICS, Vol. 25, No. 1 (2011) pp 280-305. [MR2801230]
  36. There are more strategy-proof procedures than you think, (with Jerry Kelly and Donald Campbell), MATHEMATICAL SOCIAL SCIENCES, Vol. 64 No. 3 (2012) pp 263-265.
  37. Fullerene patches II (with Christy Graves and Steve Graves), to appear in ARS MATHEMATICA COMTEMPORANEA
  38. Clar and Fries numbers for benzenoids, (with Liz Hartung and Ahmad Souid), to appear in THE JOURNAL OF MATHEMATICAL CHEMISTRY.