# Strongly regular graph

## Concept in graph theory / From Wikipedia, the free encyclopedia

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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.

**Quick Facts**Graph families defined by their automorphisms, → ...

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 |

Close

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 − 2*k* + μ, *v* − 2*k* + 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.