Rank-3 graphs on 2401 vertices

There exist precisely ten rank-3 strongly regular graphs on 2401 vertices. They are $H(2,49)$, the Paley graph $P_{2401}$, the Peisert graph on 2401 vertices, the Van Lint-Schrijver graph on 2401 vertices, the $\mathrm{VO}_4^-(7)$ graph, the $\mathrm{VO}_4^+(7)$ graph, and the four graphs below.

Graph with valency 240

Number of vertices:$2401$
Diameter:$2$
Intersection array:$\{240,180;1,20\}$
Spectrum:$240^1 44^{240} (-5)^{2160}$
Automorphism group:$7^4:6.\mathrm{O}(5,3)$
Distance-transitive:Yes
Primitive

Graph with valency 480

Number of vertices:$2401$
Diameter:$2$
Intersection array:$\{480,360;1,90\}$
Spectrum:$480^1 39^{480} (-10)^{1920}$
Automorphism group:$7^4:6.\left(2^4:\mathrm{S}_5\right)$
Distance-transitive:Yes
Primitive

Graph with valency 720

Number of vertices:$2401$
Diameter:$2$
Intersection array:$\{720,490;1,210\}$
Spectrum:$720^1 34^{720} (-15)^{1680}$
Automorphism group:$7^4:6.\mathrm{S}_7$
Distance-transitive:Yes
Primitive

Graph with valency 960

Number of vertices:$2401$
Diameter:$2$
Intersection array:$\{960,570;1,380\}$
Spectrum:$960^1 29^{960} (-20)^{1440}$
Automorphism group:$7^4:48.\mathrm{S}_5$
Distance-transitive:Yes
Primitive




Downloads (Valency 240)

Downloads (Valency 480)

Downloads (Valency 720)

Downloads (Valency 960)

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Last updated: 23 July 2024