
Department
School
Research Interest
Graph theory and its applications, random networks, fuzzy logic, theoretical computer science and category theory
Publications
Book:
John Mordeson, Kiran R. Bhutani and Azriel Rosenfeld, “Fuzzy Group Theory”, Springer-Verlag, 2005.
Recent publications:
1) Bhutani, K., Kalpathy, R., Mahmoud, H., and Ofonedu, A. (2023). Some empirical and theoretical attributes of random multi-hooking networks. International Journal of Computer Mathematics: Computer Systems Theory, 8:4, 222-234. DOI: 10.1080/23799927.2023.2278098
2) 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
3) Bhutani, K., Kalpathy, R., and Mahmoud, H. (2023). Degrees in random m-ary hooking networks. Compositionality, Volume 5, Issue 6, 1-21. DOI: 10.32408/
4) 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
5) (2021) Average measures in polymer graphs, International Journal of Computer Mathematics: Computer Systems Theory, 6:1, 37-53, DOI: 10.1080/23799927.2020.1860134
6) Manju Raju, Kiran R. Bhutani and S. Arumugam: Changing and unchanging of F-Domination number of a graph,” Journal of Discrete Mathematical Sciences & Cryptography (submitted).
7) Raju, M., Bhutani, K. R., Moazzez, B., & Arumugam, S. (2020). Algorithmic Aspects of F-Domination in Graphs. Utilitas Mathematic, 116, 169-176.
8) (2018) On F-domination in graphs, AKCE International Journal of Graphs and Combinatorics, 17:1, 60-64, DOI: 10.1016/j.akcej.2018.07.004.
9) 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.
10) 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
Other Activities
- Currently, Dr. Ravi Kalpathy and I mentor an undergraduate student on a research project in random networks funded by the College of Arts and Sciences.
- In summer 2020, along with Dr. Curtis Holliman and Dr. Ravi Kalpathy, I mentored four undergraduates in summer research projects which were funded by the College of Arts and Sciences and the School of Engineering.
- In 2018, 2019, and 2021, I 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.
- A Minor in Actuarial Sciences (jointly with the Busch School of Business, implemented fall ’17)
- An accelerated B.S./M.S. (4+1) program in Math Secondary Education (jointly with the Department of Education, implemented fall ’17)
- An accelerated B.S./M.S. (4+1) in Mathematics (implemented fall ’18)
- A Minor in Data Analysis (jointly with the School of Engineering, implemented fall ’18)
- A Minor in Statistics (implemented in Spring '20)
- A Minor in Mathematical Finance (implemented spring ’20)
- A B.S. in Mathematical Finance (implemented spring ’20).
University Service: I serve or have served in various capacities for my Department, for the College of Arts and Sciences, and for the University. I was a member (2004-2007) and a current alternate member (2007 - present) of the Committee on Appointment and Promotion for the College of Arts and Sciences, a former member of the Search Committee for a new Dean (2016), a current member of the Unit Standards Committee (2019-present), the inaugural Chair of the first Part-time Faculty Committee (2015 - 2018), as well as many more throughout the course of my University career.