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, R. Pellico, I. Renteria, and S. Vora. Well-edge-dominated graphs containing triangles, submitted (2025)
  9. B. Brešar, K. Kuenzel, and D. F. Rall. Claw-free graphs are (1,1,2,2)-colorable, Discrete Math., 347, Issue 5: 114477 (2025)
  10. K. Kuenzel and D. F. Rall. A characterization of well-dominated Cartesian products, Discrete Math., 347, Issue 5: 113904 (2024)
  11. B. Brešar, T. Dravec, D. P. Johnston, K. Kuenzel, and D. F. Rall. Isolation game on graphs, Graphs and Combin., 42(30): (2026) https://doi.org/10.1007/s00373-026-03030-y
  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. W. Goddard, K. Kuenzel, and E. Melville. Well-hued graphs, Discrete Applied Math., 320: 370-380 (2022)
  26. 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)
  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)