Strongly regular graph: Difference between revisions

Revision as of 17:45, 3 October 2023

Revision as of 09:58, 5 October 2023

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{{Graph families defined by their automorphisms}}

In [[graph theory]], a '''strongly regular graph''' ('''SRG''') is a [[regular graph]] {{math|1=''G'' = (''V'', ''E'')}} with {{mvar|v}} vertices and [[Degree (graph theory)|degree]] {{mvar|k}} such that for some given integers <math>\lambda, \mu \ge 0</math>

* every two [[adjacent vertices]] have {{math|λ}} common neighbours, and

* every two non-adjacent vertices have {{math|μ}} common neighbours,.

for some integers <math>\lambda, \mu \ge 0.</math>

The [[complement graph|complement]] ofSuch a strongly regular graph is also strongly regular. The complement of andenoted {{math|srg(''v'', ''k'', λ, μ)}}. Its [[complement graph|complement]] is analso strongly regular: {{math|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 {{math|1=λ = 1}}.