Graph theory and its applications, random networks, fuzzy logic, theoretical computer science and category theory
John Mordeson, Kiran R. Bhutani and Azriel Rosenfeld, “Fuzzy Group Theory”, Springer-Verlag, 2005.
1) Bhutani, K., Kalpathy, R., and Mahmoud, H. (2023). Random multi-hooking networks. Probability in the Engineering and Informational Sciences, 1-15. DOI: 10.1017/ S0269964822000523
2) Bhutani, K., Kalpathy, R., and Mahmoud, H. (2022). Random networks grown by fusing edges via urns. Network Science, 1-14. DOI: 10.1017/nws.2022.30
3) (2021) Average measures in polymer graphs, International Journal of Computer Mathematics: Computer Systems Theory, 6:1, 37-53,
4) Manju Raju, Kiran R. Bhutani and S. Arumugam: Changing and unchanging of F-Domination number of a graph,” Journal of Discrete Mathematical Sciences & Cryptography (to appear).
5) Raju, M., Bhutani, K. R., Moazzez, B., & Arumugam, S. (2020). Algorithmic Aspects of F-Domination in Graphs. Utilitas Mathematica, 116, 169-176.
6) (2018) On -domination in graphs, AKCE International Journal of Graphs and Combinatorics, 17:1, 60-64, .
7) Rashmi, S. D., Arumugam, S., Bhutani, K. R., & Gartland, P. (2017). Perfect secure domination in graphs. Categories and General Algebraic Structures with Applications, 7(Special Issue on the Occasion of Banaschewski's 90th Birthday (II)), 125-140.
8) Arumugam, S., Bhutani, Kiran and Sathikala, L., (2016), On (r,s)-Fuzzy Domination in Fuzzy Graphs, New Mathematics and Natural Computation (NMNC), 12, issue 01, p. 1-10, DOI: 10.1142/S1793005716500010
- Currently Dr. Ravi Kalpathy and I are mentoring an undergraduate student on a research project in random networks funded by the School of Arts & Sciences.
- In summer 2020, I, along with Dr. Curtis Holliman and Dr. Ravi Kalpathy, mentored four undergraduates in summer research projects which were funded by the School of Arts & Science and the School of Engineering.
- In 2018, 2019 and 2021, mentored undergraduate students in research in graph theory. They presented their findings at the Catholic University of America’s annual Research Day and made it to the list of finalists.
University Service: I have served in various capacities for my Department, for the School of Arts & Sciences and the University: member (2004-2007) and alternate member (2007 - present) of the Committee on Appointment and Promotion of A&S, Dean Search Committee (spring 2016), Unit Standards Committee (2019-present), Chair of the first Part-time Faculty Committee (2015 - 2018), and more.