jopix2.jpg (12204 bytes) S. M. C.
Department of Mathematics
Saint Michael's College
Winooski Park
Colchester, VT  05439


phone: 802 654 2660
fax: 802 654 2610
WB01542_.gif (729 bytes) Click here for alter ego.
Jo Ellis-Monaghan

Contact me On Campus Courses Advising
Student Research My Research Papers Talks
St. Mike's Links Other Stuff Vita  

On Campus

Office:  St. Edmunds 217A.  Office hours Fall 2009:  MTu 1:00-2:00, and other times by appointment.    

Some classes from prior semesters (Most courses after about 2006 have been ported to e-College, so that material isn't available here.  Feel free to contact me if there is something specific you would like.)

Student Research: 


Design Strategies for Self-Assembling Nanostructures.

This is an ongoing project involving a number of students over the years.

June 2009-May 2010 outcomes (primarily supported by the CURM, but also VSGC and VGN).


Here are some recent student publications  (also see the publication list where student coauthors are indicated by an asterisk):

·         L. Beaudin, “A review of the Potts model:  its relation to the Tutte polynomial and its application to complex experiments,”  The Rose-Hulman Undergraduate Math Journal, 8 no. 1, 2007. Co-advised with G. Pangborn.

·         A. Austin, “The circuit partition polynomial, with applications and relation to the Tutte and interlace polynomials,” The Rose-Hulman Undergraduate Math Journal, 8 no. 2, 2007.

·         J. Kaptcianos, “A graph theory approach to DNA fragment assembly,” American Journal of Undergraduate Research, 7 no.1, 2008. Kap08.pdf


Here are a few sample presentations (mostly PowerPoint) by past and current students--talks from Senior Seminars,  Hudson River, Parents' Weekend, and some Independent Study results.  Note:  The mathematics in some of the presentations requires MathType to be viewed properly.  



Doctorate in Mathematics:  University of North Carolina, Chapel Hill, NC.   fall 1995.  Advisor: James D. Stasheff.

Areas of Research :  Algebra and Combinatorics.

I am interested in both graph theory and abstract algebra, particularly in using algebraic techniques to achieve graph theoretic results. My recent work has been primarily with graph polynomials, constructing them and embedding them in algebraic structures sufficiently rich to extract new information from them. I have been able to use Hopf-algebras to derive new identities for the Martin polynomials of both oriented and unoriented Eulerian graphs, as well as for the Tutte polynomial along the diagonal y = x.  My interests also include applications of graph theory to problems arising from computer chip design and from DNA sequencing and biomolecular computing.

Talks with available overheads:  

PDF and/or Postscript files are available for the overheads for some of my talks. PDF files require Adobe Acrobat ReaderPostscript files can be viewed and printed using Ghostview, which is available on line--click here to go to the site.  The mathematics in some of the PowerPoint presentations requires MathType to be viewed properly.  

NIMBioS Graph theory in the life sciences NIMBios workshop on graph theory in biology, 8/16/2010. Graph Theory in the life sciences.pdf

NIMBioS Design strategies for DNA nanostructures, NIMBios workshop on graph theory in biology, 8/16/2010.  nanostructure design strategies.pdf

Graph Theory and Complex Systems in Statistical Mechanics.  SMC/UVM joint applied combinatorics seminar, 10/23/08. UVM Potts

The Increasingly Popular Potts Model, or, A Graph Theorist Does Physics.  WIMIN Conference, Smith College,  9/27/08. A graph theorist does physics

Graph Theory Designs for DNA Nanostructures, REU Program, SUNY Pottsdam, 7/22/08.  Tile Types

Multivariable Tutte and Transition Polynomials, Combinatorics and Statistical Mechanics Programme at the Isaac Newton Institute for the Mathematical Sciences, Cambridge University. April 2008.   multivariable extensions 2.pdf  Video at

Graph Models for DNA Structures, Villanova, 10/1/07.  Graph Models DNA.ppt, Graph Models DNA.pdf

Minimum Tile Types. MathFest 2007, San Jose, 8/5/07.  Talks/Minimum tile types.pdf

A Little Statistical Mechanics for the Graph Theorist.  South Eastern, Boca Raton, 3/9/07. A Little Stat Mech.pdf

From Potts to Tutte and back again:  A graph theoretical view of statistical mechanics, (with applications).  UPenn 11/15/06.  The Potts-Tutte model3.pdf

An introduction to the Potts Model.  SMC/UVM joint applied combinatorics seminar, 10/26/06. Intro to Potts.pdf

From Potts to Tutte and back again:  A graph theoretical view of statistical mechanics.  Middlebury College, 10/27/05. From Potts to Tutte and back again.ppt, From Potts to Tutte and back again 4.pdf

Weak Tutte Functions of Matriods, 2nd Workshop on the Tutte Polynomial and its Applications, 10/5/05.  Weak Tutte Functions of Matroids.pdf (scanned notes for 'chalk talk')

A Duality Relation for the Topological Tutte Polynomial, AMS Eastern Section Meeting Special Session on Graph and Matroid Invariants,  Bard College, 10/9/05. A Duality Relation.pdf  (scanned overheads)

Graph models for DNA structures, Vermont Genetics Network Workshop 8/17/05. DNA struct (html), DNA struct.pdf, DNA struct.ppt

Properties of the interlace polynomial, AMS Pittsburgh, 11/7/04.  interlace properties.pdf

Graph models from the Kevin Bacon game to biomolecular computing and beyond!  Skidmore Colloquium, 10/20/04.  Graph Models 3.pdf, Graph Models 3.ppt

Crazy Cubes and other applications of graphs and networks.  UVM highschool contest awards ceremony, 5/6/04 Crazy CubesUVM.pdf or CrazyCubesUVM.ppt

Graph Theoretical Problems in Next Generation Chip Design.  South Eastern, Boca Raton, 3/3/03. [Graphs in chip design--PowerPoint]

A Hopf-algebraic structure for generalized transition polynomials.  Special Session on Combinatorial Hopf Algebras at the AMS meetings in Montreal, QC, 5/5/2002 [abstract and ps file--583 KB]

Independent Studies with Industry Partnership.  MathFest 2002, Burlington VT.  [PowerPoint--461 KB]

Practical Applications and the Universality of the Tutte Polynomial.  UVM Colloqium Talk, 2/15/2002.  [Links]

Relations for Skein-Type Graph Polynomials.  South Eastern, Baton Rouge, 2/26/2001.  [Abstract]  [Click here for postscript file--866 KB].

The Circuit Partition Polynomial and Integer Evaluations of the Tutte Polynomial.  CoNE, Smith College, 2/10/2001.   [Click here for postscript file--1550 KB]  (sorry so large--26 color slides done in Word take up a lot of space....)  Proofs for much of what was covered in this talk can be found in Identities for the Circuit Partition Polynomials... below.


[Research]  [Pedagogy]

PDF and/or  Postscript files are available for several of these papers.  PDF files require Adobe Acrobat Reader.   Postscript files can be viewed and printed using Ghostview, which is available on line--click here to go to the site.  If any paper is not available electronically, or if any fail to download properly, please email me directly for a copy.

Student coauthors are indicated with as undergraduate* and graduate#.


  1. J. Ellis-Monaghan, I. Moffatt, Twisted duality for embedded graphs, in press, Transactions of the American Mathematical Society.

  2. J. Ellis-Monaghan, I. Moffatt, The Tutte-Potts connection in the presence of an external magnetic field, Advances in Applied Mathematics, 47 (2011)

  3. J. Ellis-Monaghan, I. Sarmiento, “A recipe theorem for the topological Tutte polynomial of Bollobás and Riordan," European Journal of Combinatorics 32 no 6 ( 2011) 782–794.

  4. L. Beaudin*, J. Ellis-Monaghan, G. Pangborn, R. Shrock, A little statistical mechanics for the graph theorist, Discrete Mathematics, 310 (13-14)  2010, 2037-2053.

  5.   J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications I: the Tutte polynomial, invited chapter for Structural Analysis of Complex Networks, Matthias Dehmer, ed., Birkhauser, 2010.

  6. J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications II: interrelations and interpretations, invited chapter for Structural Analysis of Complex Networks, Matthias Dehmer, ed., Birkhauser, 2010.

  7.  A. Dean, J. Ellis-Monaghan, S. Hamilton*, G. Pangborn, Unit rectangle visibility graphs,”The Electronic Journal of Combinatorics, 15, no. 1 (2008) R79.

  8. M. Cox#, J. Ellis-Monaghan, T. Hughes, K. Mondanaro, Hydrocarbon links in an octet truss, The Journal of Mathematical Chemistry, 43, no. 2 (2008) 874-891.

  9. J. Ellis-Monaghan, I. Sarmiento, Distance hereditary graphs and the interlace polynomial,  Combinatorics, Probability and Computing., 16, no.6 (2007) 947-973

  10. J. Ellis-Monaghan, P. Gutwin, J. Lewis*, G. Pangborn, Principles of force directed floorplanning, submitted. (PDF--133 KB)

  11. D. Archdeacon, P. Bonnington, J. Ellis-Monaghan, How to exhibit toroidal maps in space,” Discrete and Computational Geometry, 38, (2007) 573-594ABE-M07.pdf

  12. J. Ellis-Monaghan, I. Sarmiento, Isotropic systems and the interlace polynomial,”submitted.

  13. J. Ellis-Monaghan, D. Pike, Y. Zou#, Decycling of Fibonacci cubes, The Australasian Journal of Combinatorics 35 (2006), 31-40. E-MPZ06.pdf

  14. J. Ellis-Monaghan, P. Gutwin, J. Lewis*, G. Pangborn, “Force-directed floorplanning with flexible blocks,”  Congressus Numerantium, 178 (2006) 147-15 E-MGLP06.pdf

  15. J. Ellis-Monaghan, L. Traldi, Parameterized Tutte polynomials of weighted graphs and matroids.  Combinatorics, Probability, and Computing 15 (2006) 835-854. E-MT06.pdf    This version includes detailed computations for prop. 7.2 left to the reader in the submitted version.  (PDF--192 KB)  (details.pdf)

  16. J. Ellis-Monaghan, P. Gutwin, J. Lewis*, G. Pangborn, “Principles of force directed floorplanning,” Congressus Numerantium, 175 (2005), 81-96  E-MGLP05.pdf

  17.  J. Ellis-Monaghan, Transition Polynomials, Double Covers, and Biomolecular Computing, Congressus Numerantium, 166 (2004) 181-192(PDF--169 KB)

  18. D. Archdeacon, J. Ellis-Monaghan, D. Fisher, D. Froncek, P. C. B. Lam, S. Seager, B. Wei, and R. YusterSome remarks on domination, Journal of Graph Theory, 46 no 3 (2004) 207-210  AE-MFFLSWY04.pdf

  19.  J. Ellis-Monaghan,  Exploring the Tutte-Martin connection, Discrete Mathematics, 281, no 1-3 (2004) 173-187. E-M04a.pdf  [click here for postscript file--799 KB]  

  20.  J. Ellis-Monaghan, Identities for the circuit partition polynomials, with applications to the diagonal Tutte polynomial, Advances in Applied Mathematics, 32 no. 1-2, (2004) 188-197. E-M04b.pdf [Click here for postscript file--305 KB].  

  21.  J. Ellis-Monaghan and P. Gutwin Graph Theoretical Problems in Next Generation Chip Design, Congressus Nu me rantium, 163 (2003) 143-159. E-MG03.pdf   [click here for postscript file--810 KB]  

  22.  J. Ellis-Monaghan and I. Sarmiento, Generalized transition polynomials, Congressus Numerantium 155 (2002) 57-69. E-MS02.pdf  [click here for postscript file--491 KB].

  23.  J. Ellis-Monaghan and I. Sarmiento,  Medial graphs and the Penrose polynomial, Congressus Numerantium 150 (2001), 211–222. E-MS01.pdf [click here for postscript file--2 files]   

  24.  J. Ellis-Monaghan, Differentiating the Martin polynomial.   Congressus Numerantium 142 (2000), 173–83.  E-M00.pdf  [click here for postscript file--449 KB]

  25.  J. Ellis-Monaghan, Martin polynomial miscellanea. Congressus Numerantium 137 (1999), 19–31.  E-M99.pdf   [click here for postscript file--481 KB]

  26.  J. Ellis-Monaghan, New results for the Martin polynomial. Journal of Combinatorial Theory, series B 74 (1998), 326–52. E-M98a.pdf


  1.  J. Ellis-Monaghan, G. Pangborn, “Using DNA self-assembly design strategies to motivate graph theory concepts,”  Math. Model. Nat. Phenom., 6, no. 6 (2011) 96-107.

  2. G. Ashline, J. Ellis-Monaghan, Z. Kadas, D. McCabe, “Math and Bio 2010: Shell morphology overview and poster,”   MAA Focus, 30 (3), 2010, 15-17.
  3. J. Ellis-Monaghan, "Considering the chalkless classroom," PRIMUS, 20 (4), 2010, 332 – 343. E-Mpre.pdf

  4. G. Ashline, J. Ellis-Monaghan, Z. Kadas, D. McCabe, “Modeling seashell morphology,” UMAP Module 801. In UMAP/ILAP Modules 2009: Tools for Teaching, edited by Paul J. Campbell, 101-139  AE-MKMpre.pdf

  5. G. Ashline, K-D. Crisman, J. Ellis-Monaghan, Z. Kadas, G. Pangborn, L. Simons, “What we learned…by organizing and hosting an MAA sectional meeting”,  MAA Focus, April/May 2009    AE-MKPS09.pdf          .

  6. G. Ashline, J. Ellis-Monaghan, “How high?  How fast?  How long?  Modeling water rocket flight with calculus,” PRIMUS XVI, no. 2 (2006), 121-137  AE-M06.pdf

  7. G. Ashline, J. Ellis-Monaghan, “A house of your own: The mathematics of the American dream, part II,” The New Jersey Mathematics Teacher 63 no. 2 (2005)  20-26. AE-M05a.pdf

  8. G. Ashline, J. Ellis-Monaghan, “Credit cards and cars: The mathematics of the American dream, part I,” The New Jersey Mathematics Teacher, 63 no. 1 (2005) 16-23. AE-M05b.pdf

  9. A. Daniels*, J. Ellis-Monaghan, Surreal Seashells, The Pi Mu Epsilon Journal, 12 no. 1 (2004) 36. DE-M04.pdf

  10. G. Ashline, J. Ellis-Monaghan, The lottery: A dream co me true or a tax on people who are bad at math?   PRIMUS XIV no. 4 (2004) 303-314.  AE-M04.pdf

  11. G. Ashline, A. Brizard, and J. Ellis-Monaghan, Water rockets in flight: Calculus in action, UMAP/ILAP Modules, 2002-2003: Tools for Teaching.  151-189. ABE-M02-03.pdf

  12. G. Ashline, J. Ellis-Monaghan, Home sweet home: A financial incentive for the lower level mathematics course, PRIMUS XI, no. 1 (2001), 16–26. AE-M01.pdf

  13. G. Ashline, J. Ellis-Monaghan, How many people are in your future? Elementary models of population growth,  in Making meaning: Integrating science through the case study approach to teaching and learning, ed. S. Kuntz et al,  McGraw-Hill Primis, 1999, pp. 42–80. AE-M99a.pdf

  14. G. Ashline, J. Ellis-Monaghan, How many people are in your future? Elementary models of population growth (updated version), Case studies in ecology, ed. S. Kuntz et al., accompanying the 1st editions of Manuel Molles’ text Ecology: Concepts and Applications. WCB McGraw-Hill, New York, 1999. AE-M99a.pdf

  15. G. Ashline, J. Ellis-Monaghan, Interdisciplinary population projects in a first semester calculus course, PRIMUS IX (March 1999), 39–55. AE-M99c.pdf

  16. G. Ashline, J. Ellis-Monaghan, Microcosm to macrocosm: Population models in biology and demography, Tools for Teaching, UMAP unit 777 (1999), 39–80. AE-M99d.pdf

Saint Michael's-related links

For more information, you may want to check out these.

Other Stuff

UVM/SMC Joint  Combinatorics Seminar  Biweekly speakers from academia and industry using and developing combinatorial techniques.

Maple Home Page   Very, very cool Maple stuff--including lots of demos for understanding calculus concepts for example.  Check out the Maple Applications and the Student pages. Gorgeous math/science art pictures with explainations.

MathSciNet   This is the foremost research tool for mathematicians--a searchable index, with reviews, to current mathematical articles.  Very cool applet for generating celtic knots

Graph Theory Resources   This site has links to people, problems, journals, etc. involved with graph theory.

Math Archives This is a huge archive of all kinds of math related resources, from teaching resources to CAS (eg Maple) support, from graphing calculators to electronic journals.

POPMathematics   What is POP Mathematics?  From the site creators:   Check out this web site for lots of people doing cool (math-related) things you might be interested in too.

Actuarial Careers  Here are some links providing information about actuarial careers.

The following website has some great explanations and good Java applets for a wide range of mathematical concepts.

Some info on math learning styles: MathLearningProfiles.pdf, MathMethodsDyslexia.pdf

The wallpaper on this page was modified from wallpaper taken from where there are lots of other very lyrical wallpapers.

When this site was last updated: