CV

Appointments

Associate Professor of Mathematics – Trinity College    July 2024 – present

Assistant Professor of Mathematics – Trinity College    July 2019 – June 2024

Assistant Professor of Mathematics – Western New England University   Aug. 2017 – July 2019

Harold L. Dorwart Visiting Assistant Professor – Trinity College   July 2014 – June 2017

Postdoctoral Researcher – University of Johannesburg   May 2014 – Aug. 2014

Education

Ph.D.   Clemson University, Clemson SC         Advisors: Wayne Goddard (Clemson) and Douglas F. Rall (Furman)

MS       Texas State University, San Marcos, TX      Advisor: Diana Gu

BS        University of Texas at Austin, Austin, TX

Editorial Activities

  • On the editorial board of Involve, a journal of mathematics

Publications

  1. P. Dorbec, T. Dravec, T. James, and K. Kuenzel, Domination game: from Rall’s 1/2-Conjecture to chordal graphs, submitted (2026)
  2. S. E. Anderson, K. Kuenzel, and J. Marcano-Cuellar, Diamond-free, claw-free, cubic graphs are (1, 1, 2, 3)-colorable, submitted (2026)
  3. S. E. Anderson and K. Kuenzel, A characterization of all nonbipartite well-edge-dominated graphs, submitted (2026)
  4. S. E. Anderson and K. Kuenzel, Characterizing all K4-free well-edge-dominated graphs of girth 3, submitted (2026)
  5. B. Brešar, T. Dravec, D. P. Johnston, K. Kuenzel, D. F. Rall, and A. Tepeh, Isolation number: Cartesian and lexicographic products and generalized Sierpinski graphs, Discrete Math., in press
  6. B. Brešar, T. Dravec, K. Kuenzel, and D. F. Rall, On Maker-Breaker domination game critical graphs, Discrete App. Math., in press
  7. G. Boyer, K. Kuenzel, J. Lyle, and R. Pellico, Well-hued graphs with first difference two, submitted (2025)
  8. J. Berg, P. Chang, C. Kaneshiro, K. Kuenzel, I. Renteria, and S. Vora. Well-edge-dominated graphs containing triangles, submitted (2025)
  9. B. Brešar, K. Kuenzel, and D. F. Rall. Claw-free cubic graphs are (1,1,2,2)-colorable, Discrete Math., 347, Issue 5: 114477 (2025)
  10. B. Brešar, T. Dravec, D. P. Johnston, K. Kuenzel, and D. F. Rall. Isolation game on graphs, Graphs and Combin., 42(30): (2026)
  11. K. Kuenzel and D. F. Rall. A characterization of well-dominated Cartesian products, Discrete Math., 347, Issue 5: 113904 (2024)
  12. M. Han, S. Herlihy, K. Kuenzel, D. Martin, and R. Schmidt. The number of independent sets in bipartite graphs and benzenoids, Aequat. Math. (2024) https://doi.org/10.1007/200010-024-01124-7
  13. A. Domat and K. Kuenzel. Loop zero forcing and Grundy domination in planar graphs and claw-free cubic graphs, Bull. Malays. Math. Sci. Soc., 47 (10) (2024) https://doi.org/10.1007/s40840-024-01705-4
  14. S. E. Anderson, T. Dravec, D. P. Johnston, and K. Kuenzel. Orientable total domination in graphs, submitted (2023)
  15. G. Bacso, B. Brešar, K. Kuenzel, and D. F. Rall. Graphs with equal Grundy domination and independence number, Discrete Optim., 48 (2): 100777 (2023)
  16. S.E. Anderson, K. Kuenzel, and H. Schuerger. Graphs which satisfy a Vizing-like bound for the power domination of Cartesian products, submitted (2022)
  17. S.E. Anderson, B. Brešar, S. Klavžar, K. Kuenzel, and D.F. Rall. Orientable domination in product-like graphs. Discrete App. Math., 326: 62-69 (2023)
  18. K. Kuenzel and D.F. Rall. On independent domination in direct products.  Graphs and Combin., accepted (2022)
  19. S.E. Anderson and K. Kuenzel. Power domination in cubic graphs and Cartesian products. Discrete Math., 345(11): 113113 (2022)
  20. J.P. Georges, K. Kuenzel, D.W. Mauro, and P.S. Skardal. On a distance-constrained graph labeling to model cooperation, Discrete App. Math., 306: 17 – 31 (2022) 
  21. B. Brešar, K. Kuenzel, and D.F. Rall. Domination in digraphs and their products. J. Graph Theory: 99(3): 359-377 (2022)
  22. S.E. Anderson, K. Kuenzel, and D.F. Rall. On well-edge-dominated graphs. Graphs and Combin., 38(106) (2022)
  23. S.E. Anderson and K. Kuenzel. Independent transversal domination in trees, products, and under local changes to a graph. Aequat. Math., 96: 981-995 (2022)
  24. S.E. Anderson, K. Kuenzel, and D.F. Rall. On well-dominated graphs. Graphs and Combin., 37(1): 151-165 (2021)
  25. B. Brešar, B. Hartnell, M.A. Henning, D.F. Rall, and K. Wash. A new framework to approach Vizing’s conjecture, Discuss. Math. Graph Theory, 41(3): 749-762 (2021)  (DOI :10.7151/dmgt.2293)
  26. W. Goddard, K. Kuenzel, and E. Melville. Well-hued graphs, submitted (2020)
  27. W. Goddard, K. Kuenzel, and E. Melville. Graphs in which all maximal bipartite subgraphs have the same order, Aequat. Math., 94: 1241-1255 (2020)
  28. B. Brešar, K. Kuenzel, and D.F. Rall. Graphs with a unique maximum open packing, Indian Journal of Discrete Mathematics, 5(1): 37-55 (2019)
  29. K. Kuenzel and D.F. Rall. On well-covered direct products, Discuss. Math. Graph Theory, to appear (DOI :10.7151/dmgt.2296)
  30. B. Hartnell, D.F. Rall, and K. Wash. On well-covered Cartesian products, Graphs and Combin., 34: 1259-1268 (2018)
  31. S.E. Anderson, S. Nagpal, and K. Wash. Domination in the hierarchical product and Vizing’s conjecture, Discrete Math., 341(1): 20-24 (2018)
  32. B. Brešar, S. Klavžar, D.F. Rall, and K. Wash. Packing chromatic number versus chromatic and clique number,  Aequat. Math., 92(3): 497-513 (2017)
  33. B. Brešar, S. Klavžar, D.F. Rall, and K. Wash. Packing chromatic number, (1,1,2,2)-colorings, and characterizing the Petersen graphs, Aequat. Math., 91(1): 169-184 (2017)
  34. B. Brešar, S. Klavžar, D.F. Rall, and K. Wash. Packing chromatic number under local changes in a graph, Discrete Math., 340(5): 1110-1115 (2017)
  35. M.A. Henning and K. Wash. Matchings, path covers and domination, Discrete Math., 340(1): 3207-3216 (2017)
  36. D.F. Rall and K. Wash. On minimum identifying codes in some Cartesian product graphs, Graphs and Combin., 33(4): 1037-1053 (2017)
  37. J.P Georges, D. Mauro, and K. Wash. On zero-sum Z_{2j}^k-magic graphs, J. Combin. Optim. 34(1): 94-113 (2017)
  38. S.E. Anderson, Y. Guo, A. Tenney, and K. Wash. Prime factorization and domination in the generalized hierarchical product, Discuss. Math. Graph Theory, 37(4): 873-890 (2017)
  39. P.S. Skardal and K. Wash. Spectral properties of the hierarchical product of graphs, Physical Review E  94, 052311 (2016)
  40. M.A. Henning and K. Wash. Trees with large neighborhood total domination number, Discrete Applied Math., 187: 96-102 (2015)
  41. W. Goddard, K. Wash, and H. Xu. WORM colorings, Discuss. Math. Graph Theory, 35: 571-584 (2015)
  42. W. Goddard, K. Wash, and H. Xu. WORM colorings forbidding cycles or cliques, Congressus Numerantium, (2014)
  43. K. Wash. Edgeless graphs are the only universal fixers, Czech. Math., 64(139): 833-843 (2014)
  44. D.F. Rall and K. Wash. Identifying codes of the direct product of two cliques, European J. of Combin., 36: 159-171 (2014)
  45. W. Goddard and K. Wash. ID codes in Cartesian products of cliques, J. Combin. Math. Combin. Comput., 85: 97-106 (2013)
  46. W. Gu and K. Wash. Bounds on the domination number of permutation graphs, J. Interconnection Networks, 10(3): 205-217 (2009)

Publications with Students

  1. C. Cooper and K. Wash. t-tone colorings in the Cartesian product, Congressus Numerantium (2017)
  2. A. Fong, J.P. Georges, D. Mauro, D. Spagnuolo, J. Wallace, S. Wang, and K. Wash. On the zero-sum group-magicness of Cartesian products, Involve, Vol. 12: 1261-1278 (2019)
  3. J. Loe, D. Middlebrooks, A. Morris, and K. Wash. 2-tone colorings in graph products, Discuss. Math. Graph Theory, 37(4): 873-890 (2017)
  4. J. Brown, A. Hasmani, L. Hiltner, A. Kraft, D. Scofield, and K. Wash. On the computation of all characteristic p extensions of a p-adic field of a given degree, Rocky Mountain Math Journal, 45 No. 1 (2015)

Undergraduate Research Advising

I have been a research mentor at the Yale SUMRY REU for the summers of 2023, 2024, and 2026. Additionally, I have advised the following research projects for Trinity students.

2025/2026: I am the thesis adviser to Manuela Rodes. We are using graphs to study algebraic extensions of free groups. 

Summer 2025 research advisees: Audra Pilkington and Juan Marcano Cuellar. Audra was able to show that the line graphs of certain well-edge-dominated graphs are spanning subgraphs of BG graphs (and therefore not counterexamples to Vizing’s conjecture). Juan was able to contribute an original contribution to the 3 Decomposition conjecture – an impenetrable problem involving edge decompositions of cubic graphs. 

2024/2025: I advised Diarra Sadji, an environmental science major conducting an interdisciplinary research project in chemical graph theory. We compared the ratio associated with the Merrifield-Simmons index to imperical data taken from software used in the Chemistry Department for a group of benzenoids.

Summer 2024 research advisee: Maxwell Cooper. Maxwell studied the class of well-totally-dominated graphs.

Summer 2023 research advisee: Shash Sunkum. Shash helped revive an old project with John Georges and David Mauro where we studied the domination number of the Cartesian product of 3 cliques.

Spring 2023: I advised Faith Bailey in an independent study in chemical graph theory. We found bounds for the Merrifield-Simmons index in caterpillars.

2022: I advised Alex Domat in his summer research project. We studied the grundy domination number and loop zero forcing number of particular graph classes. 

2020/2021: I advised Div Gaur’s senior thesis titled Power domination in cubic graphs

2018/2019: I advised Henry Wix’s senior thesis titled Applications of Integer Programming: Graph Domination and RK Puzzles.

2016/2017: Jack Wallace did an independent study on Algebraic Geometry and formulating combinatorial problems in the context of Algebraic Geometry. I also advised Catherine Cooper’s senior thesis on $t$-tone colorings in the Cartesian product of graphs.

Summer 2016:  My research advisees were Jacqueline Kromasch and Shriya Nagpal. Jacqueline studied using PCA, LDA, and k-means clustering to identify common manufacturing sources among 82 counterfeit pharmaceutical pills. Shriya’s project was on improving upon the class of graphs that satisfy Vizing’s Conjecture. Shriya presented her work at MathFest and won the Cur Award for her presentation.

Summer 2015:  My research advisees were Yaoqi Guo and Asa Tenney. Asa studied domination in the hierarchical product of graphs. He presented his work at MathFest and won an Outstanding Presentation Award.

Summer 2013: I was a research advisor in the Clemson REU in Combinatorics, Computational Algebraic Geometry, and Number Theory. My group studied 2-tone colorings in graph products. The students presented their work at the Southeast REU Conference. 

Summer 2012: I was a graduate student mentor in the Clemson REU in Combinatorics, Computational Algebraic Geometry, and Number Theory. My group studied classifying local fields of characteristic p. The students presented their work at the Southeast REU Conference.                                                            

Honors and Awards

  • AMS Simons Research Enhancement Grants for PUI Faculty – 2024 – 2027
  • Faculty Research Expense Grant from Trinity College – 2024 – 2025
  • Slovenia/USA Bilateral Research Grant 2016 – present
  • Waitlisted for an AMS-Simons Travel Grant 2015
  • AWM Travel Grant March 2015 and June 2017

  • Professional Enrichment Grant, Clemson University, April 2013

  • AMS Travel Grant, March 2013

  • Professional Enrichment Grant, Clemson University, January 2013

  • Excellence in Teaching Award, Department of Mathematical Sciences, Clemson University, May 2012

Service

  • Serving on the Faculty Research Committee at Trinity AY 24/25, 25/26, and 26/27 (chair AY 25/26 and 26/27)
  • Serving on the Committee for Institutional Advancement at Trinity AY 26/27, 27/28 and 28/29
  • Serving on the Academic Freedom Committee at Trinity AY 26/27 and 27/28
  • Faculty Sponsor For Trinity’s AWM Student Chapter
  • Program Chair for the MAA Northeastern Section Meeting hosted at Trinity Fall 2016