Finite Orthogonal Graphs

Hyperbolic Orthogonal Graphs

GraphNo. of vertices
$\mathrm{O}_4^+(2)$ graph $\cong$ Paley graph $P_9$9
$\mathrm{O}_6^+(2)$ graph $\cong$ Grassmann graph $J_2(4,2)$35
$\mathrm{O}_8^+(2)$ graph135
$\mathrm{O}_6^+(4)$ graph357
$\mathrm{O}_{10}^+(2)$ graph527
$\mathrm{O}_6^+(5)$ graph806
$\mathrm{O}_8^+(3)$ graph1120
$\mathrm{O}_{12}^+(2)$ graph2079

Parabolic Orthogonal Graphs

GraphNo. of vertices
$\mathrm{O}_5(2)$ graph $\cong \mathrm{Sp}_4(2)$ graph15
$\mathrm{O}_7(2)$ graph $\cong \mathrm{Sp}_6(2)$ graph63
$\mathrm{O}_9(2)$ graph $\cong \mathrm{Sp}_8(2)$ graph255
$\mathrm{O}_7(3)$ graph364
$\mathrm{O}_{11}(2)$ graph $\cong \mathrm{Sp}_{10}(2)$ graph1023
$\mathrm{O}_9(3)$ graph3280
$\mathrm{O}_7(5)$ graph3906

Elliptic Orthogonal Graphs

GraphNo. of vertices
$\mathrm{O}_6^-(2)$ graph $\cong$ Point graph of $\mathrm{GQ}(2,4)$27
$\mathrm{O}_6^-(3)$ graph $\cong$ Point graph of $\mathrm{GQ}(3,9)$112
$\mathrm{O}_8^-(2)$ graph119
$\mathrm{O}_6^-(4)$ graph $\cong$ Point graph of $\mathrm{GQ}(4,16)$325
$\mathrm{O}_{10}^-(2)$ graph495
$\mathrm{O}_6^-(5)$ graph $\cong$ Point graph of $\mathrm{GQ}(5,25)$756
$\mathrm{O}_8^-(3)$ graph1066

Complements

GraphNo. of vertices
$\overline{\mathrm{O}_8^+(2)}$ graph135

Back to: A-Z index • Graphs by family
Last updated: 13 August 2024