RICHARD HAMMACK
Virginia Commonwealth University
Department of Mathematics and Applied Mathematics
1015 Floyd Ave.
Richmond, Virginia 23284-2014
4146 Harris Hall
804-828-6237
rhammack @ vcu . edu
www.people.vcu.edu/~rhammack

EDUCATION:

PhD in Mathematics, 1996

University of North Carolina
at Chapel Hill

MS in Computer Science
, 1988

Virginia Commonwealth University
Richmond, Virginia


BFA in Painting
, 1983

Rhode Island School of Design
Providence, Rhode Island


EMPLOYMENT:
BOOKS:

 

Handbook of Product Graphs, Second edition
by Richard Hammack, Wilfried Imrich and Sandi Klavzar
CRC Press - Taylor and Francis Group,
Series: Discrete Mathematics and its Applications
2011.

Click on title for more information.

Book of Proof (2nd edition)
by Richard Hammack
2013.


Click on title for more information.

AWARDS:
  • Recipient: UNC Tanner Award For Excellence in Undergraduate Teaching, 1997
  • Recipient: UNC J. Burton Linker Award for Excellence in Teaching, May 1993
  • Nominee: VCU College of Humanities and Sciences Distinguished Teaching Award, 2017
  • Nominee: VCU College of Humanities and Sciences Distinguished Lecturer Award, 2015
  • Nominee: VCU College of Humanities and Sciences Excellence in Scholarship Award, 2013
  • Nominee: Tanner Award For Excellence in Undergraduate Teaching, 1994
  • Nominee: Tanner Award For Excellence in Undergraduate Teaching, 1993

RESEARCH PUBLICATIONS:
  1. Graph bases and diagram commutativity (with Paul Kainen), under review.
  2. Vertex-transitive direct products of graphs, (with Wilfried Imrich), under review.
  3. Robust cycle bases do not exist for Kn,n when n ≥ 8, (with Paul Kainen), Discrete Applied Mathematics, 235, 206–211, 2018.
  4. Neighborhood reconstruction and cancellation of graphs, (with Cristina Mullican), Electronic Journal of Combinatorics, 24(2) 2017.
  5. Proper Connection of Direct Products of Graphs (with Dewey Taylor), Discussiones Mathematicae Graph Theory, 37(4) 1005–1013, 2017.
  6. Cycle bases of reduced powers of graphs (with Greg Smith), Ars Mathematica Contemporanea, 12(1): 183–202, 2017.
  7. Associativity and Non-Associativity of Some Hypergraph Products (with Marc Hellmuth, Lydia Ostermeier and Peter Stadler) Mathematics in Computer Science, 10(3): 403–408, 2016.
  8. Edge Transitive Products (with Wilfried Imrich and Sandi Klavzar), Journal of Algebraic Combinatorics, 43(4) 837–850, 2016.
  9. A prime factor theorem for bipartite graphs, (with Owen Puffenberger), European Journal of Combinatorics, 47: 123–140, 2015.
  10. Fast recognition of direct and strong products (with Wilfried Imrich), Ars Mathematica Contemporanea, 7: 487–497, 2014.
  11. Zero divisors among digraphs (with Heather Smith), Graphs and Combinatorics, 30(1), 171–181, 2014.
  12. Cancellation of digraphs over the direct product, European Journal of Combinatorics, 34: 846–858, 2013.
  13. On uniqueness of prime bipartite factors of graphs, Discrete Mathematics, 313: 1018–1027, 2013. (Here is my own version, identical but better formatted.)
  14. Frucht's theorem for the digraph factorial, Discussiones Mathematicae Graph Theory, 33: 329 –336, 2013.
  15. Notes on the independence number in the Cartesian product of graphs (with Ghidewon Abay-Asmerom, Craig Larson and Dewey Taylor), Discussiones Mathematicae Graph Theory, 31(1) 25–35, 2011.
  16. The inner power of a graph (with Neal Livesay), Ars Mathematica Contemporanea, 3: 193–199, 2010.
  17. An isomorphism theorem for digraphs (with Laura Culp), Australasian Journal of Combinatorics, 48: 205–211, 2010.
  18. Cancellation of direct products of digraphs (with Katherine Toman), Discussiones Mathematicae Graph Theory, 30(4): 575–590, 2010.
  19. A quasi cancellation property for the direct product, Discrete Mathematics, 310: 1691–1696, 2010.
  20. Direct product factorization of bipartite graphs with bipartition-reversing involutions (with Ghidewon Abay-Asmerom, Craig Larson and Dewey Taylor), SIAM Journal on Discrete Mathematics, 23(4): 2042–2052, 2010.
  21. On Cartesian skeletons of graphs (with Wilfried Imrich), Ars Mathematica Contemporanea, 2(2): 191–205, 2009.
  22. Proof of a conjecture concerning the direct product of bipartite graphs, European Journal of Combinatorics (Special Issue on Metric Graph Theory), 30: 1114–1118, 2009.
  23. Minimum cycle bases of direct products of graphs with cycles (with Zachary Bradshaw), Ars Mathematica Contemporanea, 2(1): 101–119, 2009.
  24. Factorial properties of graphs (with Ghidewon Abay-Asmerom and Dewey Taylor), Australasian Journal of Combinatorics, 44: 265–272, 2009.
  25. On direct product cancellation of graphs, Discrete Mathematics, 309: 2538–2543, 2009.
  26. Perfect r-codes in strong products of graphs (with Ghidewon Abay-Asmerom and Dewey Taylor), Bulletin of the ICA, 55: 66–72, 2009.
  27. Unique prime Cartesian Factorization of graphs over a finite field, Missouri Journal of Mathematical Sciences, 21(3): 149–154, 2009.
  28. Complementary composition of graphs (with Ghidewon Abay-Asmerom and Dewey Taylor), Congressus Numernatium, 189: 113–120, 2008.
  29. A cancellation property for the direct product of graphs, Discussiones Mathematicae Graph Theory, 28(1) 179–185, 2008.
  30. Total perfect codes in tensor products of graphs (with Ghidewon Abay-Asmerom and Dewey Taylor), Ars Combinatoria, 88: 129–234, 2008.
  31. Fractional graphs, Australasian Journal of Combinatorics, 39: 135–140, 2007.
  32. Minimum cycle bases of direct products of complete graphs, Information Processing Letters, 102: 214–218, 2007.
  33. Isomorphic components of direct products of bipartite graphs, Discussiones Mathematicae Graph Theory, 26(2): 231–248, 2006
  34. Minimum cycle bases of direct products of bipartite graphs, Australasian Journal of Combinatorics, 36: 13–26, 2006.
  35. Square contractions of graphs, Australasian Journal of Combinatorics, 36: 213–221, 2006.
  36. Centers of tensor products of graphs, (with Ghidewon Abay-Asmerom), Ars Combinatoria, 74: 201–211, 2005.
  37. Centers of n-fold tensor products of graphs, (with Sarah Bendall), Discussiones Mathematicae: Graph Theory, 24: 491–501, 2004.
  38. Equitable chromatic number of complete multipartite graphs, (with Dorothee Blum and Denise Grittner), Missouri Journal of Mathematical Sciences, 15: 75–81, 2003.
  39. A note on the complexity of computing cyclicity, Ars Combinatoria, 63:89–95, 2002.
  40. Cyclicity of graphs, Journal of Graph Theory, 32(2): 160–170, 1999.
  41. Circularity of planar graphs, Houston Journal of Mathematics, 25(2): 213–221, 1999.
TEACHING AND EXPOSITORY PUBLICATIONS:
  1. A geometric view of complex trigonometric functions, College Mathematics Journal, 38(3): 210–217, May 2007.
  2. Alternating Series Convergence: A visual proof (with David Lyons), Teaching Mathematics and its Applications, 25(2): 58–60, 2006.
  3. An informal approach to formal inner products, Missouri Journal of Mathematical Sciences, 17: 153–160, 2005.
  4. Proof Without Words (with David Lyons), College Mathematics Journal, 32(1): p 72, 2005.
  5. A simple way to teach logarithms (with David Lyons), Mathematics Teacher, 88(5): 374–375, 1995.

SELECTED TALKS AND PRESENTATIONS:
  1. Not every graph has connected sum basis, Knots in Washington XLIV, The George Washington University, Washington DC, April 28, 2017.
  2. Not every graph has a robust cycle basis, LSU Graduate Mathematics Seminar, Baton Rouge, LA, March 9, 2017.
  3. Neighborhood reconstruction and cancellation of graphs, LSU Combinatorics Seminar, Baton Rouge, LA, March 8, 2017.
  4. Integrate THIS: The mathematics of planimeters, LSU Undergraduate Mathematics Colloquium, Baton Rouge, LA, March 7, 2017.
  5. Integrate THIS: The mathematics of planimeters, SIAM Mathematics Awareness Conference, Old Dominion University, Norfolk, VA, April 9, 2016.
  6. The fourth dimension, Mu Alpha Theta Induction, Maggie L. Walker Governor's School, Richmond, VA, March 9, 2016.
  7. Edge transitive products, AMS Special Session on Graph Products, AMS-MAA Joint Meetings, Seattle, WA, January 9, 2016.
  8. Automorphism groups of bipartite direct products, 8th Slovenian International Conference on Graph Theory, Kranjska Gora, Slovenia, June 23, 2015.
  9. Non-Euclidean geometry and the visual arts, Pi Mu Epsilon Induction Ceremony, Lebanon Valley College, Annville, PA, April 18, 2015.
  10. Prime factorization of graphs over the direct product, (On-line speaker) Instructional Workshop in Graph Theory, Christ University, Bangalore, India, March, 2015.
  11. When can we cancel? Special Session: New Developments in Graph Theory, AMS Sectional meeting, Greensboro, NC, November, 2014.
  12. A prime factor theorem for bipartite graphs, Special Session: Recent Trends in Graph Theory, AMS-MAA Joint Meetings, Baltimore, MD, January, 2014.
  13. A do-it-yourself guide to on-demand publishing, Special Session on Open Source Textbooks, AMS-MAA Joint Meetings, Baltimore, MD, January, 2014.
  14. Did Caravaggio use a camera?, Mathematics Colloquium, Randolph-Macon College, October 25, 2013.
  15. Direct product cancellation of digraphs, Special Session: Recent Trends in Graph Theory, AMS-MAA Joint Meetings, Boston, MA, January 6, 2012.
  16. The factorial of a digraph, Mathematics Colloquium, University of Richmond, October 25, 2011.
  17. The factorial of a graph, Special Session: New Developments in Graph Theory, AMS Sectional meeting, Wake Forest University, September 25, 2011.
  18. Factoring direct products of graphs via Cartesian skeletons, Seminar: Montanuniversität Leoben, Leoben, Austria, July 30, 2010.
  19. Prime factorization of bipartite graphs over the direct product, Seminar: University of Maribor, Maribor, Slovenia, July 30, 2010.
  20. Non-Euclidean geometry and the visual arts, Pi Mu Epsilon Induction Ceremony, Randolph-Macon College, April 30, 2010.
  21. An aspect of direct product cancellation of digraphs, Algebraic Graph Theory 2009, Dubrovnik, Croatia, June 1, 2009.
  22. Isomorphic components of direct products of bipartite graphs II , Joint Meetings of the MAA and AMS, Washington D.C., January 8, 2009.
  23. The anamorphic image, Randolph-Macon College, October 17, 2008.
  24. Direct product cancellation, 46th Midwest Graph Theory Conference, West Virginia University, Morgantown WV, April 26, 2008.
  25. A quasi cancellation property for the direct product, Sixth Slovenian International Conference on Graph Theory, Lake Bled, Slovenia, June 25, 2007.
  26. Minimum cycle bases of direct products of bipartite graphs, Joint Meetings of the MAA and AMS, New Orleans, LA, January 7, 2007.
  27. What does a graph fraction look like? MAA MD-VA-DC Section Meeting, Longwood University, Farmville, VA, November 4, 2006.
  28. Visual proof of the Alternating Series Test, MAA VA-MD-DC Section meeting, University of Virginia, April 2, 2005.
  29. Contracting graphs to squares, Joint Meetings of the MAA and AMS, Atlanta, GA, January 7, 2005.
  30. A complement criterion for cyclicity, National Meeting of the MAA, Providence, RI, August 14, 2004.
  31. Integrate THIS: The mathematics of planimeters, R-MC Mathematics Department Colloquium, May 5, 2004.
  32. Centers of tensor products of graphs, National Joint Meeting of AMS and MAA, Baltimore, MD, January 17, 2003.
  33. An informal approach to formal inner products, MAA MD-VA-DC Section Meeting, University of Maryland, College Park, November 1, 2002.
  34. Recent results in cyclicity, Virginia Commonwealth University Mathematics Colloquium, November 7, 2001.
  35. Cyclicity of products, Fourth N.C. Mini-Conference on Graph Theory, Combinatorics, and Computing, Appalachian State University, Boone, N.C., April 16, 1999.
  36. Using computer graphics to visualize meromorphic functions on Riemann surfaces, MAA Southeastern Section Meeting, Rhodes College, Memphis, Tenn., March 12, 1999.
  37. Circularity of planar graphs, MAA Southeastern Section Meeting, College of Charleston, Charleston, S.C., March 13, 1998.

PROFESSIONAL MEMBERSHIPS:
  1. American Mathematical Society
  2. Mathematical Association of America