|Graph families defined by their automorphisms|
|symmetric (arc-transitive)||t-transitive, t ≥ 2|
|vertex- and edge-transitive||edge-transitive and regular||edge-transitive|
A graph of this kind is sometimes said to be an srg(v,k,λ,μ).
Some authors exclude graphs which satisfy the definition trivially, namely those graphs which are the disjoint union of one or more equal-sized complete graphs, and their complements, the Turán graphs.
A strongly regular graph is a distance-regular graph with diameter 2, but only if μ is non-zero.