3 papers
math.CO2026
On The Secure Domination of Mycielskian Graphs
Kiran R. Bhutani, Anthony Christiana, Peter Ulrickson
We study the secure domination number of the Mycielskian graph of a simple, connected, undirected graph. We give generally applicable bounds, compute secure domination numbers for…
math.PR2023
Degrees in random -ary hooking networks
Kiran R. Bhutani, Ravi Kalpathy, Hosam Mahmoud
The theme in this paper is a composition of random graphs and Pólya urns. The random graphs are generated through a small structure called the seed. Via Pólya urns, we study the as…
math.PR2022
Random multi-hooking networks
Kiran R. Bhutani, Ravi Kalpathy, Hosam Mahmoud
We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermine…