Minimal Prime Graphs of Solvable Groups [article]

Chris Florez, Jonathan Higgins, Kyle Huang, Thomas Michael Keller, Dawei Shen
2020 arXiv   pre-print
We explore graph theoretical properties of minimal prime graphs of finite solvable groups. In finite group theory studying the prime graph of a group has been an important topic for the past almost half century. Recently prime graphs of solvable groups have been characterized in graph theoretical terms only. This now allows the study of these graphs with methods from graph theory only. Minimal prime graphs turn out to be of particular interest, and in this paper we pursue this further by
more » ... ng, among other things, diameters, Hamiltonian cycles and the property of being self-complementary for minimal prime graphs. We also study a new, but closely related notion of minimality for prime graphs and look into counting minimal prime graphs.
arXiv:2011.10403v1 fatcat:b32grgljnjfl3p3afpxkqev6u4