Kiran Bhutani's Headshot

Department

  • Mathematics and Statistics

    • School

  • College of Arts and Sciences

    • 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/compositionality-5-6

    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) Kiran Bhutani, Ravi Kalpathy & Hosam Mahmoud (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) Manju Raju, Kiran R. Bhutani, Babak Moazzez & S. Arumugam (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

    Perspectives on the Pandemic: Participated in a webinar, "What History, Politics, and Math Teach Us about COVID-19" with four colleagues from CUA 
     
    Undergraduate Research: I actively encourage students to engage in undergraduate research, and to present their work to a broader audience.
    • 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.
    New Programs in the Department: Under my leadership, the Mathematics and Statistics Department has developed many new programs:
    • 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).
    These programs attract many students from different disciplines and prepare them for excellent careers in the STEM fields. The Department explores how mathematical knowledge can support interdisciplinary work in STEM areas. As Department Chair, I fund and promote innovations in teaching to help students improve their math skills and succeed in their majors.  Such innovations have included the implementation of a summer Online Pre-Calulus Review Course, the coordination of multi-section classes, the creation of a Math Center to provide support for all students in math classes, and the introduction of a summer study program for high school students called Applied Math in Action!  Our Department is also developing an online pre-stats course to introduce students to essential statistical concepts for today's age of big data and data analytics. 

    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.