Kiran Bhutani's Headshot


  • Mathematics
  • School

  • School of Arts and Sciences
  • Research Interest

    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. 

    Recent publications:

    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) 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

    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 Mathematica116, 169-176.

    6) Manju Raju, Kiran R. Bhutani, Babak Moazzez & S. Arumugam (2018) On -domination in graphs, AKCE International Journal of Graphs and Combinatorics, 17:1, 60-64, DOI: 10.1016/j.akcej.2018.07.004.

    7) Rashmi, S. D., Arumugam, S., Bhutani, K. R., & Gartland, P. (2017). Perfect secure domination in graphs. Categories and General Algebraic Structures with Applications7(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

    Other Activities

    Perspectives on the Pandemic: On June 4, 2020, along with four other faculty at CUA, I participated in a webinar, "What History, Politics, and Math Teach Us about COVID-19." 
    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 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.
    New Programs in the Math Department: Under my leadership, the Mathematics Department has developed many new STEM programs: a minor in actuarial sciences (jointly with business school, implemented fall ’17), B.S./M.S. 4+1 program in math secondary education (jointly with Education Department, implemented fall ’17), 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 and a minor in mathematical finance (implemented spring ’20), and a major in mathematical finance (implemented spring ’20). These programs have attracted a diverse body of students from different majors, preparing them for excellent careers in STEM fields. The Department is looking into how knowledge in mathematics can be transferred for developing interdisciplinary work in STEM areas. As department chair, I supported and funded innovations in teaching to help students in STEM strengthen their math skills and succeed in their majors.
    Innovations include: Online Pre-calculus Review Course, course coordination of multi-section courses, creation of Math Center to provide support in all math courses, and Applied Math in Action! high school summer program. We are also in the process of developing a pre-stats online course to help students understand the basic statistical ideas needed in this age of big data and data science. 

    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.