$\text{Diameter-2 distance-regular graphs (strongly regular graphs)}$

$\text{No. of vertices}$$\text{Intersection Array}$$\text{Parameters } (n,k,\lambda,\mu)$$\text{Graph}$
$5$$\{2,1;1,1\}$$(5,2,0,1)$$\text{Paley graph }P_5$
$6$$\{4,1;1,4\}$$(6,4,2,4)$$\text{Octahedron}$
$9$$\{4,2;1,2\}$$(9,4,1,2)$$\text{Paley graph }P_9$
$10$$\{3,2;1,1\}$$(10,3,0,1)$$\text{Petersen graph}$
$10$$\{6,2;1,4\}$$(10,6,3,4)$$J(5,2)$
$13$$\{6,3;1,3\}$$(13,6,2,3)$$\text{Paley graph }P_{13}$
$15$$\{8,3;1,4\}$$(15,8,4,4)$$J(6,2)$
$15$$\{6,4;1,3\}$$(15,6,1,3)$$K(6,2)$
$16$$\{5,4;1,2\}$$(16,5,0,2)$$\text{Clebsch graph}$
$16$$\{6,3;1,2\}$$(16,6,2,2)$$\text{Shrikhande graph}$
$16$$\{9,4;1,6\}$$(16,9,4,6)$$\text{Complement of Shrikhande graph}$
$16$$\{6,3;1,2\}$$(16,6,2,2)$$H(2,4)$
$16$$\{9,4;1,6\}$$(16,9,4,6)$$\text{Complement of }H(2,4)$
$16$$\{10,3;1,6\}$$(16,10,6,6)$$\text{Complement of Clebsch graph}$
$17$$\{8,4; 1,4\}$$(17,8,3,4)$$\text{Paley graph }P_{17}$
$21$$\{10,4;1,4\}$$(21,10,5,4)$$J(7,2)$
$21$$\{10,6;1,6\}$$(21,10,3,6)$$K(7,2)$
$25$$\{8,4;1,2\}$$(25,8,3,2)$$H(2,5)$
$25$$\{12,6; 1,6\}$$(25,12,5,6)$$\text{Paley graph }P_{25}$
$25$$\{12,6;1,6\}$$(25,12,5,6)$$\text{Paulus graphs on 25 vertices}$
$26$$\{10,6;1,4\}$$(26,10,3,4)$$\text{Paulus graphs on 26 vertices}$
$26$$\{15,6;1,9\}$$(26,15,8,9)$$\text{Complements of Paulus graphs on 26 vertices}$
$27$$\{10,8;1,5\}$$(27,10,1,5)$$\text{Complement of Schl}\ddot{a} \text{fli graph}$
$27$$\{16,5;1,8\}$$(27,16,10,8)$$\text{Schl}\ddot{a} \text{fli graph}$
$28$$\{12,5;1,4\}$$(28,12,6,4)$$J(8,2)$
$28$$\{15,8;1,10\}$$(28,15,6,10)$$K(8,2)$
$28$$\{12,5;1,4\}$$(28,12,6,4)$$\text{Chang graphs}$
$28$$\{15,8;1,10\}$$(28,15,6,10)$$\text{Complement of Chang graphs}$
$29$$\{14,7; 1,7\}$$(29,14,6,7)$$\text{Paley graph }P_{29}$
$35$$\{18,8;1,9\}$$(35,18,9,9)$$\text{Grassmann graph }J_2(4,2)$
$36$$\{14,6;1,4\}$$(36,14,7,4)$$J(9,2)$
$36$$\{21,10;1,15\}$$(36,21,10,15)$$K(9,2)$
$36$$\{10,5;1,2\}$$(49,12,5,2)$$H(2,6)$
$37$$\{18,9; 1,9\}$$(37,18,8,9)$$\text{Paley graph }P_{37}$
$40$$\{12,9;1,4\}$$(40,12,2,4)$$\text{Point graphs of }GQ(3,3) \text{ and its dual}$
$41$$\{20,10; 1,10\}$$(41,20,9,10)$$\text{Paley graph }P_{41}$
$45$$\{12,8;1,3\}$$(45,12,3,3)$$\text{Point graph of }GQ(4,2)$
$45$$\{16,7;1,4\}$$(45,16,8,4)$$J(10,2)$
$45$$\{28,12;1,21\}$$(45,28,15,21)$$K(10,2)$
$49$$\{24,12; 1,12\}$$(49,24,11,12)$$\text{Paley graph }P_{49}$
$49$$\{12,6;1,2\}$$(36,10,4,2)$$H(2,7)$
$50$$\{7,6;1,1\}$$(50,7,0,1)$$\text{Hoffman-Singleton graph}$
$53$$\{26,13; 1,13\}$$(53,26,12,13)$$\text{Paley graph }P_{53}$
$56$$\{10,9;1,2\}$$(56,10,0,2)$$\text{Gewirtz graph}$
$61$$\{30,15; 1,15\}$$(61,30,14,15)$$\text{Paley graph }P_{61}$
$64$$\{14,7;1,2\}$$(64,14,6,2)$$H(2,8)$
$73$$\{36,18; 1,18\}$$(73,36,17,18)$$\text{Paley graph }P_{73}$
$77$$\{16,15;1,4\}$$(77,16,0,4)$$M_{22} \text{ graph}$
$81$$\{20,18;1,6\}$$(81,20,1,6)$$\text{Brouwer-Haemers graph}$
$81$$\{40,20; 1,20\}$$(81,40,19,20)$$\text{Paley graph }P_{81}$
$81$$\{16,8;1,2\}$$(81,16,7,2)$$H(2,9)$
$89$$\{44,22; 1,22\}$$(89,44,21,22)$$\text{Paley graph }P_{89}$
$97$$\{48,24; 1,24\}$$(97,48,23,24)$$\text{Paley graph }P_{97}$
$100$$\{18,9;1,2\}$$(100,18,8,2)$$H(2,10)$
$100$$\{22,21;1,6\}$$(100,22,0,6)$$\text{Higman-Sims graph}$
$100$$\{36,21;1,12\}$$(100,36,14,12)$$\text{Hall-Janko graph}$
$101$$\{50,25; 1,25\}$$(101,50,24,45)$$\text{Paley graph }P_{101}$
$112$$\{30,27;1,10\}$$(112,30,2,10)$$1^{\text{st}}\text{ subconstituent of McLaughlin graph}$
$126$$\{45,32;1,18\}$$(126,45,12,18)$$\text{Zara graph}$
$130$$\{48,27;1,16\}$$(130,48,20,16)$$\text{Grassmann graph }J_3(4,2)$
$144$$\{66,35;1,30\}$$(144,66,30,30)$$\text{Halved Leonard graph}$
$155$$\{42,24;1,9\}$$(155,42,17,9)$$\text{Grassmann graph }J_2(5,2)$
$162$$\{105,32;1,60\}$$(162,105,72,60)$$2^{\text{nd}}\text{ subconstituent of McLaughlin graph}$
$175$$\{72,51;1,36\}$$(175,72,20,36)$$\text{Distance-2 graph of line graph of Hoffman-Singleton graph}$
$176$$\{70,51;1,34\}$$(176,70,18,34)$$\text{SRG(176,70,18,34)}$
$176$$\{105,36;1,54\}$$(176,105,68,54)$$\text{SRG(176,105,68,54)}$
$231$$\{30,20;1,3\}$$(231,30,9,3)$$\text{Cameron graph}$
$243$$\{22,20;1,2\}$$(243,22,1,2)$$\text{Berlekamp-van Lint-Seidel graph}$
$275$$\{112,81;1,56\}$$(275,112,30,56)$$\text{McLaughlin graph}$
$416$$\{100,63;1,20\}$$(416,100,36,20)$$\mathrm{G}_2(4)\text{ graph}$
$651$$\{90,56;1,9\}$$(651,90,33,9)$$\text{Grassmann graph }J_2(6,2)$

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Last updated: 14 August 2018