Strongly regular graph: Difference between revisions

Revision as of 00:25, 10 January 2025

Revision as of 08:15, 10 January 2025

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* The [[Schläfli graph]] is an srg(27, 16, 10, 8) and is the complement of the aforementioned line graph on GQ(2, 4).<ref>{{MathWorld | urlname=SchlaefliGraph | title=Schläfli graph|mode=cs2}}</ref>

* The [[Hoffman–Singleton graph]] is an srg(50, 7, 0, 1).

* The [[Sims-Gewirtz graph]] is an srg(56, 10, 0, 2).

* The [[M22 graph]] aka the [[Mesner graph]] is an srg(77, 16, 0, 4).

* The [[Brouwer–Haemers graph]] is an srg(81, 20, 1, 6).

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===Triangle-free graphs===

The strongly regular graphs with λ&nbsp;=&nbsp;0 are [[triangle-free graph|triangle free]]. Apart from the complete graphs on fewer than 3 vertices and all complete bipartite graphs, the seven listed earlier (pentagon, Petersen, Clebsch, Hoffman-Singleton, Sims-Gewirtz, Mesner-M22, and Higman-Sims) are the only known ones.

===Geodetic graphs===