Logo

Department
     Contact
     Directions
     Facilities
     History
     Photos
People
     Administration
     Faculty
     Emeriti Faculty
     Emeriti Faculty
     Visitors & PostDocs
     Grad Students
     Staff
Research
     Pure Math
     Applicable Math
     Math Education
Undergrad Program
Graduate Program
Courses
     Undergrad
     Graduate
     Current(Pdf)
Miscellaneous

Publications of Jack Graver

Books:

  1. COMBINATORICS WITH EMPHASIS ON GRAPH THEORY, (with M.E. Watkins), 351 pages, Springer-Verlag, 1977, (MR 58 #21632).
  2. INCIDENCE AND SYMMETRY IN DESIGN AND ARCHITECTURE, (with J. Baglivo), 306 pages, Cambridge University Press, 1983
  3. COMBINATORIAL RIGIDITY, (with B&H. Servatius), Volume 2 in the AMS series Graduate Studies in Mathematics, 1993. (MR95b: 52034)
  4. COUNTING ON FRAMEWORKS: MATHEMATICS TO AID IN THE DESIGN OF RIGID STRUCTURES, Number 25 in the Dolciani Mathematical Expositions, Mathematical Association of America, 2001, 192 pages.

Expository Papers

  1. Combinatorial Mathematics in the High School Curriculum, published in two parts, N.Y. STATE MATH. TEACHERS JOURNAL, Vol. XIX, No. 2, (April 1969), pp. 52-57, No. 3 (June 1969), pp. 118-129.
  2. Ramsey Theory, by Graham, Rothschild, and Spencer, an invited book essay THE MATHEMATICAL INTELLIGENCER, Vol. 3, No. 4, 1981, pp.191-3
  3. A Summary of Results from Mean Distance for Shapes, (with J.K. Doyle), invited by ENVIRONMENT AND PLANNING B, Vol. 9, No. 2, 1982, pp.174-7.
  4. A book review of the Open University's course "Graphs, Networks, and Designs" ENVIRONMENT AND PLANNING B, Vol. 9, No. 4, 1983, pp.496-497.
  5. An alternative approach to the dimension theorem for inner products, THE AMERICAN MATHEMATICAL MONTHLY, Vol. 94, No. 7, 1987, pp. 671-679.
  6. Programmable Graphics Calculators in the Classroom: A Report on One Experience, by invitation, to The City University of New York annual, MATHEMATICS IN COLLEGE, 1990, pp. 39-43.
  7. Using the Sharp EL-5200 Calculator in Mathematics, 53 pages, Published by Coply Publishing., 1990
  8. Student Guide for ISP 121, Elements of Modern Mathematics, 134 pages. Published by Syracuse Univ., 1992.
  9. Locally Finite, Planar, Edge-transitive Graphs, GRAPH THEORY NOTES OF NEW YORK XXIV, 1993, pp. 9-16.
  10. A Geometric Approach to Linear Functions, THE COLLEGE MATHEMATICS JOURNAL, Vol. 26, No. 5, 1995, pp. 389-394
  11. Linear Functions and Rounding (with L. Lardy), a student research project, THE COLLEGE MATHEMATICS JOURNAL, Vol. 31, No. 2, Mar. 2000, pp132-6.
  12. Research Questions from Elementary Calculus (with L. Lardy), a student research project, THE COLLEGE MATHEMATICS JOURNAL, Vol. 32, No. 5, November 2001, pages 388-393.
  13. A Simple Proof of the Dimension Theorem for Inner Products, submitted.

Research Publications

  1. An Analytic Triangulation of an Arbitrary Analytic Variety, J. MATH. MECH., Vol. 13 (1964), No. 6, pp. 1021-1036, (MR 29 #5254).
  2. Lectures on the Theory of Matroids, Lecture Notes, Series C, No. 2, published by the University of Alberta.
  3. An Upper Bound for Ramsey Numbers (with James Yackel), BULL. AMER. MATH. SOC., Vol. 72 (1966), No. 6, pp. 1076-1079, (MR 33 #7270).
  4. Some Graph Theoretic Results Associated with Ramsey's Theorem (with J. Yackel), J. COMBINATORIAL THEORY, Vol. 4 (1968), No. 2, pp. 125-175, (MR 37 #1278).
  5. Remarks on the Parameters of a System of Sets, ANN. N.Y. ACAD. SCIENCE, Vol. 175 (7/3/1970), Article 1, pp. 187-198, (MR 45 #3213).
  6. 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, (MR 44 #6556)
  7. A characterization of Symmetric Block Designs, J. COMBINATORIAL THEORY, Vol. 12, No. 2 (March 1972), pp. 304-308, (MR 45 #4991).
  8. Algebra-Structures for General Designs, (with W.B. Jurkat), J. OF ALGEBRA, Vol. 23 (December 1972), No. 3, pp. 574-589, (MR 46 #8872).
  9. The Module Structure of Integral Designs, (with W.B. Jurkat), J. COMB. THEORY, Vol. 15 (July 1973), No. 1, pp. 75-90, (MR 48 #8270).
  10. Boolean Designs and Self-Dual Matroids, LINEAR ALGEBRA AND APPLICATIONS, Vol. 10, (1975), pp. 111-128, (MR 51 #12576).
  11. 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, (MR 53 #5343).
  12. On the Foundations of Linear Integer Programming I, MATHEMATICAL PROGRAMMING, Vol. 9, No. 2, October 1975, pp. 207-226, (MR 52 #7525).
  13. Mean Distance in a Graph, (with J.K. Doyle), DISCRETE MATHEMATICS, Vol. 17, No. 2, (Feb. 1977), pp. 147-154, (MR 58 #5307).
  14. Mean Distance in a Directed Graph, (with J.K. Doyle), ENVIRONMENT AND PLANNING B, Vol. 5, No. 1 (June 1978), pp. 19-30.
  15. The Imbedding Index of a Graph, J. COMBINATORIAL THEORY B, Vol. 27, No. 2 (October 1979), pp. 151-159, (MR 81d:05023).
  16. f-Factors and Related Decompositions of Graphs (with W.B. Jurkat), J. COMBINATORIAL THEORY B, Vol. 28, No. 1 (February 1980), pp. 66-84, (MR 81c:05074).
  17. Mean Distance for Shapes (with J.K. Doyle), J. GRAPH THEORY , Vol. 6, No. 4, (December 1982), pp. 453-478, (MR 84f:05079).
  18. A Combinatorial Approach to Infinitesimal Rigidity, Technical; Report #10, Department of Mathematics, Syracuse University, August 1984, 49 pages.
  19. A Characterization of Finite Planar Primitive Graphs (with M. Watkins), SCIENTIA., SER. A: MATHEMATICAL SCIENCES, Vol. 1 (1988), pp. 59-60.
  20. Rigidity Matroids, SIAM JOURNAL ON DISCRETE MATHEMATICS, Vol. 4, No. 3 (August 1991), pp.355-368. (MR 92g:05058)
  21. Abstract rigidity in m-Space, (with B&H. Servatius), CONTEMPORARY MATHEMATICS, Vol. 178 (1994), pp.145-151. (MR95j:05064)
  22. 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. (MR97i05001)
  23. Designing a Mirror that Inverts in a Circle. (with G. Cargo and J. Troutman) to appear in THE MATHEMATICAL INTELLIGENCER, 17 pages.
  24. The (m,k)-Patch Boundary Code Problem, MATCH (Communications in Mathematical and in Computer Chemistry), Vol 48 (2003) pp 189-196.
  25. A Characterization of Infinite Planar Primative Graphs, with Mark Watkins, J. COMBINATORIAL THEORY B, vol 19,N0 1(2004) pp 87-104.
  26. Encoding Fullerness and Geodesic Domes, SIAM J.DISCRETE MATH, vol 17, No. 4(2004) pp 596-614.
  27. The Structure of Fullerenes, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 69, AMS, (2005), pp137-166.
  28. A Catelog of All Fullerenes with Ten or More Symmetries, DIMACS Series in discrete Mathematics and Theoretical Computer Science, Vol.69, AMS, (2005), pp167-188.
  29. You May Rely on the Relaibility 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..
  30. The Independence number of fullerenes and benzenoids, THE EUROPEAN JOURNAL OF COMINATORICS, Vol. 27, Issue 6 (2006) pp 850-863 .
  31. Growing fullerenes from seed: growth transformations of fullerene polyhedra (with G. Brinkmann, D. Franceus and P. Fowler), CHEMICAL PHYSICS LETTERS, 428 (2006) pp 386-393.
  32. A note on natural correspondences that satisfy exclusion, SOCIAL CHOICE AND WELFARE, 29 (2007) pp 105-106.
  33. Kekule structures and face independence number of a fullerene, THE EUROPEAN JOURNAL OF COMBINATORICS, Vol. 28, Issue 4 (2007) pp 1115-1130.

Page updated 1/4/05 cg
Link to SU Home Link to College of Arts and Sciences Home