## Darren Narayan

Professor Narayan's Homepage

#### Contact Information

Office | GOS 2228 |

Phone | (585) 475-2514 |

Fax | (585) 475-6627 |

dansma@rit.edu |

#### Office Hours

Mondays 1:30-3:30 Wednesdays 1:30-3:30#### Research Interests

Graph Theory, Combinatorics, Integer Programming, Bio-Mathematics

#### Selected Publications

Refereed Research Publications

1. A. B. Evans, G. Isaak, D. A. Narayan, Representations of Graphs Modulo n, Discrete Mathematics 223, (2000) 109-123.

2. D. A. Narayan, The Reversing Number of a Digraph; A Disjoint Union of Directed Stars, Congressus Numerantium., 145, (2000) 53-64. 3. N. D. Cahill, J. R. D'Errico, D. A. Narayan and J. Y. Narayan, Fibonacci Determinants, College Mathematics Journal 33, No. 3, (2002) 221-225. 4. D. A. Narayan and A. J. Schwenk, Tiling Large Rectangles, Mathematics Magazine. 75, No. 5, (2002), 372-380. 5. J. L. Baldwin, W. C. Kronholm, and D. A. Narayan, Tournaments with a Transitive Tournament as a Feedback Arc Set, Congressus Numerantium. 158, (2002) 51-58. 6. D. A. Narayan, An Upper Bound for the Representation Numbers of Graphs with Fixed Order, Integers A12, (2003) 1-4. 7. G. Isaak and D. A. Narayan, Complete Classification of All Tournaments having a Disjoint Union of Directed Paths as a Minimum Feedback Arc Aet. Journal of Graph Theory 45, (2004) 28-47. 8. D. A. Narayan, An Application of Perfect Matchings to Surface Reconstruction, Bulletin of the Institute of Combinatorics and its Applications, 4, (2004) 42-46. 9. D. A. Narayan, Tournaments with Feedback Path Powers, Journal of Combinatorial Mathematics and Combinatorial Computing, 49 (2004), 85-96. 10. N. D. Cahill and D. A. Narayan, Fibonacci and Lucas Numbers as Tridiagonal Matrix Determinants, Fibonacci Quarterly 42 no. 3 (2004) 216-221. 11. G. Isaak and D. A. Narayan, A Classification of Tournaments with a Tournament as a Minimum Feedback Arc Set, Information Processing Letters 92 (2004) 107-111. 12. V. Kostyuk, D. A. Narayan, V. A. Williams, Minimal rankings and the arank number of a path, Discrete Math. 306 (2006), 1991-1996. 13. D. Narayan and J. Urick, Representation numbers for split graphs, their complements, stars and hypercubes, Integers A7 (2007), 1-13. 14. D. A. Narayan, On the Reversing Number of Powers of Directed Hamiltonian Paths, Utilitas Mathematica 73 (2007) 181-207. 15. W. F. Basener and D. A. Narayan, Modern applications of graph theory, Congressus Numerantium 184 (2007), 145-159. 16. D. S. Hart, J. E. Marengo, D. A. Narayan, and D. S. Ross, On the number of trailing zeros in n!, College Mathematics Journal 39 no. 2, (2008), 139-145. 17. D. A. Narayan, Powers of directed Hamiltonian paths as feedback arc sets, Journal of Combinatorial Mathematics and Combinatorial Computing, 66 (2008), 257-272. 18. D. A. Narayan, Graph theory and surface reconstruction, College Mathematics Journal 39, No 4. (2008), 301-303. 19. S. Novotny, J. P. Ortiz, and D. A. Narayan, Minimal rankings and the rank number of a path squared, Information Processing Letters (Elsevier Science), Vol 109, Issue 3, (2009) 193-198. 20. A. B. Evans, D. A. Narayan, and J. Urick, Representation of Graphs Modulo n: Some problems, Bulletin of the Institute of Combinatorics and Its Applications, Vol.56 (No.2) (2009) 85-97. 21. G. Isaak, R. Jamison, and D. A. Narayan, Greedy rankings and arank numbers, Information Processing Letters (Elsevier Science), Vol.109 (No.15) (2009) 825-827. 22. S. Novotny, J. Ortiz, and D. A. Narayan, Maximum minimal rankings for oriented graphs, Involve, Vol. 2 (2009), No. 3, 289â295. 23. J. Lind and D. A. Narayan, Real World Graph Connectivity, Teaching Mathematics and its Applications - Oxford Journals, 28, (2009) 159-161. 24. A. Agarwal, M. Lopez, and D. A. Narayan, Representation numbers for complete graphs minus a disjoint union of graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 72 (2010), 173--180. 25. J. Ortiz, H. King, A. Zemke, D. A. Narayan, and M. Hornak, Minimal k-rankings of prism graphs, Involve 3:2 (2010), 183-190. 26. A. Zemke, S. James, and D. A. Narayan, Greedy algorithms for generalized rankings of graphs, Information Processing Letters, 110 (2010), 979-985. 27. J. Lind and D. A. Narayan, Maximum Flow in Fiber-Optic Networks, Bulletin of the Institute of Combinatorics and Its Applications, 60 (2010), 91-96. 28. M. Fisher, N. Fisher, M. Fraboni, D. A. Narayan, The birank number of a graph, to appear in Congressus Numerantium, 204, (2010), 173-180. 29. R. Florez and D. A. Narayan, An optimal ranking characterization for oriented paths and cycles, Bulletin of the Institute of Combinatorics and Its Applications, 61, (2011), 97-108. 30. D. A. Narayan, Intermediate minimal rankings of graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 78, (2011), 341-348. 31. A. Agarwal, M. Lopez, and D. A. Narayan, Representation numbers and Prague dimensions for complete graphs minus a disjoint union of paths, Journal of Combinatorial Mathematics and Combinatorial Computing, 78, (2011), 97-110. 32. E. Sergel, P. Richter, A. Trah, J. Jacob, P. Curran, and D. A. Narayan, Rank numbers for some trees and unicyclic graphs, to appear in Aequationes Mathematicae (Springer), 82, numbers (1-2), (2011), 65-79. 33. R. E. Jamison and D. A. Narayan, Sum-optimal and max-optimal labelings of graphs, Information Processing Letters, 112 (2012), 26-31. 34. V. Kostyuk, and D. A. Narayan, Maximum Minimal k-rankings of Cycles, Ars Combinatoria, in press. 35. E. Ayabi, J. Jacob, R. Laskar, D. A. Narayan, ad D. Pillone, Arankings of K_m x K_n, to appear in Discussiones Mathematics Graph Theory 36. J. Lind, D. A. Narayan, and A. Lee, Contrained shortest paths in fiber-optic networks, to appear in the Bulletin of the Institute of Combinatorics and its Applications. 37. J. Lind, D. A. Narayan, Spanning trees in hierarchical and fiber-optic networks, to appear in the Bulletin of the Institute of Combinatorics and its Applications. 38. J. Lind, D. A. Narayan, Strategies for routing data in ring-connected networks, to appear in the Bulletin of the Institute of Combinatorics and its Applications. 39. M. Bilesci, M. Gutirrez-Jhong, M. Wurtz, and D. A. Narayan, Characterization of optimal rankings of paths and cycles, to appear in the Bulletin of the Institute of Combinatorics, and Its Applications,. 40. J. Lind, D. A. Narayan, Optimal matching of approvers to access requests, submitted. 41. J. Lind, D. A. Narayan, Monitoring of telecommunication and fiber-optic networks, submitted. for publication. 42. M. Short, N. Kaplan, and D. A. Narayan, Flanking numbers and the arank number of a cycle, submitted. 43. P. Richter, E. Sergel, A. Trah, J. Jacob and D. A. Narayan, Rank numbers for bent ladders, submitted for publication. 44. R. Ashley, A. Ayela-Uwangue, F. Cabrera, C. Callesano, G. Dietert, D. A. Narayan, and A. J. Schwenk, Necessary and Sufficient Conditions for Tiling with 4x6 and 5x7 Rectangles, in preparation. Peer Reviewed Interdisciplinary / Expository Publications 1. D. A. Narayan, The Experience of a Lifetime, Proceedings of the Conference on Summer Mathematics Research Programs, American Mathematical Society, J. Gallian Ed. (2000) 279-280. 2. D. A. Narayan, The Academic Job Search in Mathematics, An Applicant's Perspective, MAA FOCUS, Vol. 20, No.8, (2000), 10-11. 3. J. Narayan, S. Gordon, and D. Narayan, Rethinking the Preparation for Calculus, MAA FOCUS, Vol 22, No 3, (2002). 4. S. K. Gupta, E.C. Hensel, A. Savakis, P. Tymann, and D. A. Narayan, Partnering with Non-academic Units in Administering the EMC2 Scholars Program, Proceedings of the Northeast Regional NSF-CSEMS PIs Workshop, Teaneck, NJ, 2004, P.1. 5. N. Shenoy, Y. Pan, D. Narayan, and D. Ross, Analysis of a routing protocol for MANETs connected to the Internet, Proceedings of the First IEEE Upstate Workshop on Communications and Networking (2004), 167-171. 6. J. Narayan and D. Narayan, The Conference: Rethinking the Preparation for Calculus, MAA Notes Volume #69: A Fresh Start for Collegiate Mathematics, Rethinking the Courses Before Calculus, (2005), 3-7. 7. N. Shenoy, Y. Pan, D. A. Narayan, D. S. Ross, and C. V. Lutzer, Route Robustness of a QoS Sensitive Routing Scheme for Internet MANETs, proceedings, 2005 Globecom Conference. 8. V. Gupta, E. Hensel, A. Savakis, P. Tymann, and D. Narayan, Retaining Female and Minority Students with EMC2 Scholars Program, Proceedings of the 2005 ASEE Annual Conference & Exposition, 2005. 9. Nirmala Shenoy, Yin Pan and Darren Narayan. "Performance of a QoS sensitive Routing Scheme for Internet MANETs", Proc. of the Second International Symposium of Wireless Communication Systems 2005 (ISWCS 2005), Italy, Sept., 2005. 10. Surendra K. Gupta, Edward C. Hensel, Andreas Savakis, Paul Tymann, and Darren Narayan, Retaining STEM Students With the EMC^2 Scholars Program at RIT, Proceedings of the 9th International Conference on Engineering Education, San Juan, Puerto Rico, (2006) Session T3E, 24-26. 11. Surendra K. Gupta, Edward C. Hensel, Andreas Savakis, Paul Tymann, and Darren Narayan, Statistics on the EMC^2 Scholars Program at RIT, Proceedings, American Society for Engineering Education, St. Lawrence Section Meeting, Cornell University (2006) 12. R. Ashley, A. Ayela-Uwangue, F. Cabrera, C. Callesano, and D. A. Narayan, Research with Students from Underrepresented Groups. Proceedings of the Conference on Promoting Undergraduate Research in Mathematics, J. Gallian, Editor, American Mathematical Society, 2007, 219-222. 13. R. Cortez, D. Davenport, H. Medina, and D. Narayan, Diversity Issues in Undergraduate Research, Proceedings of the Conference on Promoting Undergraduate Research in Mathematics, J. Gallian, Editor, American Mathematical Society, 2007, 237-243. 14. S. K. Gupta, E.C. Hensel, A. Savakis, P. Tymann, and D. A. Narayan, Retention of STEM students with the EMC^2 Scholars' Program at RIT, Proceedings of the 2007 ASEE Annual Conference, 2007. 15. S. Adams and D. A. Narayan, Resources for Undergraduate Research, Mathematical Association of America Online Column, Issue No. 1. (2008) 16. K. S. Berenhaut and D. A. Narayan, Involve - A Journal of Mathematics; An interview with the founding editor, Resources for Undergraduate Research, MAA Online Column, Issue No 2. (2008) 17. D. A. Narayan, Sponsoring a Student Avenues for Obtaining Student Travel Funding, Resources for Undergraduate Research, MAA Online Column, Issue No. 5 (2009). 18. S. Adams, R. Gillman, and D. A. Narayan, Balancing the R and E of REU Programs, Resources for Undergraduate Research, MAA Online Column, Issue No. 5 (2009). 19. M. Dorff and D. Narayan, Obtaining funding and support for undergraduate research, to appear in PRIMUS.