{"id":10,"date":"2013-07-19T19:32:45","date_gmt":"2013-07-19T19:32:45","guid":{"rendered":"https:\/\/jegraver.expressions.syr.edu\/?page_id=10"},"modified":"2013-08-11T14:54:45","modified_gmt":"2013-08-11T14:54:45","slug":"biography","status":"publish","type":"page","link":"https:\/\/jegraver.expressions.syr.edu\/?page_id=10","title":{"rendered":"Research Publications"},"content":{"rendered":"
    \n
  1. An Analytic Triangulation of an Arbitrary Analytic Variety, J. MATH. MECH., Vol. 13 (1964), No. 6, pp. 1021-1036, [MR0167989]<\/li>\n
  2. An Upper Bound for Ramsey Numbers (with James Yackel), BULL. AMER. MATH. SOC., Vol. 72 (1966), No. 6, pp. 1076-1079, [MR0199120]<\/li>\n
  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].<\/li>\n
  4. ) Remarks on the Parameters of a System of Sets, ANN. N.Y. ACAD. SCIENCE, Vol. 175 \t(7\/3\/1970), Article 1, pp. 187-198, [MR0294140]<\/li>\n
  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]<\/li>\n
  6. A characterization of Symmetric Block Designs, J. COMBINATORIAL THEORY, Vol. 12, No. 2 (March 1972), pp. 304-308, [MR0295929]<\/li>\n
  7. Algebra-Structures for General Designs, (with W.B. Jurkat), J. OF ALGEBRA, Vol. 23 (December 1972), No. 3, pp. 574-589, [MR0309767]<\/li>\n
  8. The Module Structure of Integral Designs, (with W.B. Jurkat), J. COMB. THEORY, Vol. 15 (July 1973), No. 1, pp. 75-90, [MR0329930]<\/li>\n
  9. Boolean Designs and Self-Dual Matroids, LINEAR ALGEBRA AND APPLICATIONS, Vol. 10, (1975), pp. 111-128, [MR9376400]<\/li>\n
  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]<\/li>\n
  11. On the Foundations of Linear Integer Programming I<\/a>, MATHEMATICAL PROGRAMMING, Vol. 9, No. 2, October 1975, pp. 207-226, [MR0386673]<\/li>\n
  12. Mean Distance in a Graph, (with J.K. Doyle), DISCRETE MATHEMATICS, Vol. 17, No. 2, (Feb. 1977), pp. 147-154, [MR0485476]<\/li>\n
  13. Mean Distance in a Directed Graph, (with J.K. Doyle), ENVIRONMENT AND PLANNING B, Vol. 5, No. 1 (June 1978), pp. 19-30.<\/li>\n
  14. The Imbedding Index of a Graph, J. COMBINATORIAL THEORY B, Vol. 27, No. 2 (October 1979(, pp. 151-159, [MR0546857]<\/li>\n
  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]<\/li>\n
  16. Mean Distance for Shapes (with J.K. Doyle), J. GRAPH THEORY , Vol. 6, No. 4, (December 1982), pp. 453-478, [MR0679602]<\/li>\n
  17. A Characterization of Finite Planar Primitive Graphs (with M. Watkins), SCIENTIA., SER. A: MATHEMATICAL SCIENCES, Vol. 1 (1988), pp. 59-60. [MR2313048]<\/li>\n
  18. Rigidity Matroids, SIAM JOURNAL ON DISCRETE MATHEMATICS, Vol. 4, No 3 (August 1991), pp.355-368. [MR1105942]\n<\/li>\n
  19. Abstract rigidity in m-Space<\/a>, (with B&H. Servatius), CONTEMPORARY MATHEMATICS, Vol. 178 (1994), pp.145-151. [MR1310581] <\/li>\n
  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]<\/li>\n
  21. Designing a Mirror that Inverts in a Circle<\/a>, (with G. Cargo and J. Troutman) THE MATHEMATICAL INTELLIGENCER, Vol.24, No. 1 (2002), pp.4-8.<\/li>\n
  22. The (m,k)-patch boundary code problem,<\/a> MATCH \t(Communications in Mathematical and in Computer Chemistry) Vol. 48 (2003), pp 189-196. [MR1989001]<\/li>\n
  23. A characterization of infinite planar primitive graphs,<\/a> (with Mark Watkins), J. COMBINATORIAL THEORY B, Vol. 19 No. 1 (2004), pp 87-104. [MR2047533]<\/li>\n
  24. Encoding Fullerenes and Geodesic Domes,<\/a> SIAM. J. DISCRETE MATH, \tVol. 17, No. 4 (2004), pp 596-614. [MR2085216]<\/li>\n
  25. The Structure of Fullerenes,<\/a> DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 69, AMS, (2005), pp137-166. [MR2193448]<\/li>\n
  26. A catalog of fullerenes with 10 or more symmetries,<\/a> 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.] <\/li>\n
  27. You may rely on the reliability polynomial for much more than you might \texpect,<\/a> (with Milton Sobel), COMMUNICATIONS IN STATISTICS – THEORY \tAND METHODS, Vol. 34, No. 6 (2005), pp 1411-1422. [MR2162099]<\/li>\n
  28. The independence number of fullerenes and benzenoids,<\/a> THE EUROPEAN \tJOURNAL OF COMBINATORICS, Vol. 27, Issue 6 (2006) pp 850-863. \t[MR2226422]<\/li>\n
  29. Growing fullerenes from seed: growth transformations of fullerene \tpolyhedra,<\/a> (with G. Brinkmann, D. Franceus and P. Fowler), CHEMICAL PHYSICS LETTERS, 428 (2006) pp386-393.<\/li>\n
  30. A note on natural correspondences that satisfy exclusion,<\/a> SOCIAL CHOICE AND WELFARE, 29 (2007) pp105-106. [MR2318340]<\/li>\n
  31. Kekule structures and face independence number of a fullerene,<\/a> THE EUROPEAN JOURNAL OF COMBINATORICS, Vol. 28, Issue 4 (2007) pp 1115-1130. ;MR2305578]<\/li>\n
  32. Numbers of Faces in Disordered Patches,<\/a> (with Gunnar Brinkmann & Claudia Justus), JOURNAL OF MATHEMATICAL CHEMISTRY, Vol. 45. No. 2 \t(2009) pp 263-278. [MR2470459]<\/li>\n
  33. Highly Symmetric Fullerenes and Nanotubes,<\/a> (with Yvette Monachino), Symmetry in Nanostructures, a special issue of SYMMETRY: CULTURE AND SCIENCE Vol. 19, Num. 4 (2009) pp 317-340.<\/li>\n
  34. Fullerene Patches I,<\/a> (with Christy Graves), ARS MATHEMATICA COMTEMPORANEA, Vol. 3 (2010) pp109-120. [MR2643922]<\/li>\n
  35. When does a curve bound a distorted disk?<\/a> (with G. Cargo), SIAM JOURNAL OF DISCRETE MATHEMATICS, Vol. 25, No. 1 (2011) pp 280-305. [MR2801230]<\/li>\n
  36. There are more strategy-proof procedures than you think,<\/a> (with Jerry Kelly and Donald Campbell), MATHEMATICAL SOCIAL SCIENCES, Vol. 64 No. 3 (2012) pp 263-265.<\/li>\n
  37. Fullerene patches II <\/a> (with Christy Graves and Steve Graves), to appear in ARS MATHEMATICA COMTEMPORANEA<\/li>\n
  38. Clar and Fries numbers for benzenoids,<\/a> (with Liz Hartung and Ahmad \tSouid), to appear in THE JOURNAL OF MATHEMATICAL CHEMISTRY.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    An Analytic Triangulation of an Arbitrary Analytic Variety, J. MATH. MECH., Vol. 13 (1964), No. 6, pp. 1021-1036, [MR0167989] An Upper Bound for Ramsey Numbers (with James Yackel), BULL. AMER. MATH. SOC., Vol. 72 (1966), No. 6, pp. 1076-1079, [MR0199120] Some Graph Theoretic Results Associated with Ramsey’s Theorem (with J. Yackel), J. COMBINATORIAL THEORY, Vol. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":[],"_links":{"self":[{"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=\/wp\/v2\/pages\/10"}],"collection":[{"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10"}],"version-history":[{"count":44,"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=\/wp\/v2\/pages\/10\/revisions"}],"predecessor-version":[{"id":52,"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=\/wp\/v2\/pages\/10\/revisions\/52"}],"up":[{"embeddable":true,"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=\/wp\/v2\/pages\/2"}],"wp:attachment":[{"href":"https:\/\/jegraver.expressions.syr.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}