On Gruenberg-Kegel graphs and beyond

The Gruenberg–Kegel graph (or the prime graph) of a finite group $G$ is a simple graph whose vertices are the prime divisors of $|G|$, with primes $p$ and $q$ adjacent in this graph if and only if $pq$ is an element order of $G$. The concept of Gruenberg–Kegel graph proved to be very useful in finite group theory and in algebraic combinatorics as well as with connection to research of some cohomological questions in integral group rings. In this talk, we discuss recent results on characterization of finite groups by Gruenberg-Kegel graph and by isomorphism type of Gruenberg-Kegel graph as well as combinatorial properties of Gruenberg–Kegel graphs.