# The generating graph of a finite group

Colva Roney-Dougal
University of St Andrews
6 Mar 2018, 11 am - Noon, Carslaw 373, University of Sydney

## Abstract

The generating graph of a finite group $$G$$ is a graph whose vertices are the elements of $$G$$, and with an edge between $$x$$ and $$y$$ if and only if $$x$$ and $$y$$ generate $$G$$. This is clearly only an interesting object for groups that are $$2$$-generated, but fortunately a great many interesting families of groups are $$2$$-generated, including all finite simple groups. I’ll give a survey of what is currently known about the generating graph, and finish with several open problems.