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 (as we saw in Scott Harper’s recent talk) all finite simple groups. I’ll give a survey of what is currently known about the generating graph, and finish with several open problems. |