Strongly regular graph

In graph theory, a strongly regular graph (SRG) is a regular graph $G = (V, E)$ with $v$ vertices and degree $k$ such that for some given integers $\lambda ,\mu \geq 0$

every two adjacent vertices have $λ$ common neighbours, and
every two non-adjacent vertices have $μ$ common neighbours.

Such a strongly regular graph is denoted by $srg(v, k, λ, μ)$ . Its complement graph is also strongly regular: it is an $srg(v, v - k - 1, v - 2 - 2 k + μ, v - 2 k + λ)$ .

If a graph $G$ is strongly regular with $μ > 0$ , then $G$ is distance-regular with diameter 2. Likewise, if $G$ is strongly regular with $λ = 1$ , then it is locally linear.

Graph families defined by their automorphisms
distance-transitive	→	distance-regular	←	strongly regular
↓
symmetric (arc-transitive)	←	t-transitive, $t \geq 2$		skew-symmetric
↓
_{(if connected)} vertex- and edge-transitive	→	edge-transitive and regular	→	edge-transitive
↓		↓		↓
vertex-transitive	→	regular	→	_{(if bipartite)} biregular
↑
Cayley graph	←	zero-symmetric		asymmetric