The Paley graph of order 13, a strongly regular graph with parameters (13,6,2,3).
Graph families defined by their automorphisms
distance-transitive
→
distance-regular
←
strongly regular
↓
symmetric (arc-transitive)
←
t-transitive,t ≥ 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
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
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 "parameters" are the numbers in (v, k, λ, μ). Its complement graph is also strongly regular: it is an srg(v, v − k − 1, v − 2 − 2k + μ, v − 2k + λ).
A strongly regular graph is a distance-regular graph with diameter 2 whenever μ is non-zero. It is a locally linear graph whenever λ = 1.
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