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

 $\text{No. of vertices}$ $\text{Intersection Array}$ $\text{Parameters } (n,k,\lambda,\mu)$ $\text{Graph}$ $5$ $\{2,1;1,1\}$ $(5,2,0,1)$ $\text{Paley graph }P_5$ $6$ $\{4,1;1,4\}$ $(6,4,2,4)$ $\text{Octahedron}$ $9$ $\{4,2;1,2\}$ $(9,4,1,2)$ $\text{Paley graph }P_9$ $10$ $\{3,2;1,1\}$ $(10,3,0,1)$ $\text{Petersen graph}$ $10$ $\{6,2;1,4\}$ $(10,6,3,4)$ $J(5,2)$ $13$ $\{6,3;1,3\}$ $(13,6,2,3)$ $\text{Paley graph }P_{13}$ $15$ $\{8,3;1,4\}$ $(15,8,4,4)$ $J(6,2)$ $15$ $\{6,4;1,3\}$ $(15,6,1,3)$ $K(6,2)$ $16$ $\{5,4;1,2\}$ $(16,5,0,2)$ $\text{Clebsch graph}$ $16$ $\{6,3;1,2\}$ $(16,6,2,2)$ $\text{Shrikhande graph}$ $16$ $\{9,4;1,6\}$ $(16,9,4,6)$ $\text{Complement of Shrikhande graph}$ $16$ $\{6,3;1,2\}$ $(16,6,2,2)$ $H(2,4)$ $16$ $\{9,4;1,6\}$ $(16,9,4,6)$ $\text{Complement of }H(2,4)$ $16$ $\{10,3;1,6\}$ $(16,10,6,6)$ $\text{Complement of Clebsch graph}$ $17$ $\{8,4; 1,4\}$ $(17,8,3,4)$ $\text{Paley graph }P_{17}$ $21$ $\{10,4;1,4\}$ $(21,10,5,4)$ $J(7,2)$ $21$ $\{10,6;1,6\}$ $(21,10,3,6)$ $K(7,2)$ $25$ $\{8,4;1,2\}$ $(25,8,3,2)$ $H(2,5)$ $25$ $\{12,6; 1,6\}$ $(25,12,5,6)$ $\text{Paley graph }P_{25}$ $25$ $\{12,6;1,6\}$ $(25,12,5,6)$ $\text{Paulus graphs on 25 vertices}$ $26$ $\{10,6;1,4\}$ $(26,10,3,4)$ $\text{Paulus graphs on 26 vertices}$ $26$ $\{15,6;1,9\}$ $(26,15,8,9)$ $\text{Complements of Paulus graphs on 26 vertices}$ $27$ $\{10,8;1,5\}$ $(27,10,1,5)$ $\text{Complement of Schl}\ddot{a} \text{fli graph}$ $27$ $\{16,5;1,8\}$ $(27,16,10,8)$ $\text{Schl}\ddot{a} \text{fli graph}$ $28$ $\{12,5;1,4\}$ $(28,12,6,4)$ $J(8,2)$ $28$ $\{15,8;1,10\}$ $(28,15,6,10)$ $K(8,2)$ $28$ $\{12,5;1,4\}$ $(28,12,6,4)$ $\text{Chang graphs}$ $28$ $\{15,8;1,10\}$ $(28,15,6,10)$ $\text{Complement of Chang graphs}$ $29$ $\{14,7; 1,7\}$ $(29,14,6,7)$ $\text{Paley graph }P_{29}$ $35$ $\{18,8;1,9\}$ $(35,18,9,9)$ $\text{Grassmann graph }J_2(4,2)$ $36$ $\{14,6;1,4\}$ $(36,14,7,4)$ $J(9,2)$ $36$ $\{21,10;1,15\}$ $(36,21,10,15)$ $K(9,2)$ $36$ $\{10,5;1,2\}$ $(49,12,5,2)$ $H(2,6)$ $37$ $\{18,9; 1,9\}$ $(37,18,8,9)$ $\text{Paley graph }P_{37}$ $40$ $\{12,9;1,4\}$ $(40,12,2,4)$ $\text{Point graphs of }GQ(3,3) \text{ and its dual}$ $41$ $\{20,10; 1,10\}$ $(41,20,9,10)$ $\text{Paley graph }P_{41}$ $45$ $\{12,8;1,3\}$ $(45,12,3,3)$ $\text{Point graph of }GQ(4,2)$ $45$ $\{16,7;1,4\}$ $(45,16,8,4)$ $J(10,2)$ $45$ $\{28,12;1,21\}$ $(45,28,15,21)$ $K(10,2)$ $49$ $\{24,12; 1,12\}$ $(49,24,11,12)$ $\text{Paley graph }P_{49}$ $49$ $\{12,6;1,2\}$ $(36,10,4,2)$ $H(2,7)$ $50$ $\{7,6;1,1\}$ $(50,7,0,1)$ $\text{Hoffman-Singleton graph}$ $53$ $\{26,13; 1,13\}$ $(53,26,12,13)$ $\text{Paley graph }P_{53}$ $56$ $\{10,9;1,2\}$ $(56,10,0,2)$ $\text{Gewirtz graph}$ $61$ $\{30,15; 1,15\}$ $(61,30,14,15)$ $\text{Paley graph }P_{61}$ $64$ $\{14,7;1,2\}$ $(64,14,6,2)$ $H(2,8)$ $73$ $\{36,18; 1,18\}$ $(73,36,17,18)$ $\text{Paley graph }P_{73}$ $77$ $\{16,15;1,4\}$ $(77,16,0,4)$ $M_{22} \text{ graph}$ $81$ $\{20,18;1,6\}$ $(81,20,1,6)$ $\text{Brouwer-Haemers graph}$ $81$ $\{40,20; 1,20\}$ $(81,40,19,20)$ $\text{Paley graph }P_{81}$ $81$ $\{16,8;1,2\}$ $(81,16,7,2)$ $H(2,9)$ $89$ $\{44,22; 1,22\}$ $(89,44,21,22)$ $\text{Paley graph }P_{89}$ $97$ $\{48,24; 1,24\}$ $(97,48,23,24)$ $\text{Paley graph }P_{97}$ $100$ $\{18,9;1,2\}$ $(100,18,8,2)$ $H(2,10)$ $100$ $\{22,21;1,6\}$ $(100,22,0,6)$ $\text{Higman-Sims graph}$ $100$ $\{36,21;1,12\}$ $(100,36,14,12)$ $\text{Hall-Janko graph}$ $101$ $\{50,25; 1,25\}$ $(101,50,24,45)$ $\text{Paley graph }P_{101}$ $105$ $\{32,27;1,12\}$ $(105,32,4,12)$ $\text{Goethals-Seidel graph}$ $112$ $\{30,27;1,10\}$ $(112,30,2,10)$ $1^{\text{st}}\text{ subconstituent of McLaughlin graph}$ $126$ $\{45,32;1,18\}$ $(126,45,12,18)$ $\text{Zara graph}$ $130$ $\{48,27;1,16\}$ $(130,48,20,16)$ $\text{Grassmann graph }J_3(4,2)$ $144$ $\{66,35;1,30\}$ $(144,66,30,30)$ $\text{Halved Leonard graph}$ $155$ $\{42,24;1,9\}$ $(155,42,17,9)$ $\text{Grassmann graph }J_2(5,2)$ $162$ $\{105,32;1,60\}$ $(162,105,72,60)$ $2^{\text{nd}}\text{ subconstituent of McLaughlin graph}$ $175$ $\{72,51;1,36\}$ $(175,72,20,36)$ $\text{Distance-2 graph of line graph of Hoffman-Singleton graph}$ $176$ $\{70,51;1,34\}$ $(176,70,18,34)$ $\text{SRG(176,70,18,34)}$ $176$ $\{105,36;1,54\}$ $(176,105,68,54)$ $\text{SRG(176,105,68,54)}$ $231$ $\{30,20;1,3\}$ $(231,30,9,3)$ $\text{Cameron graph}$ $243$ $\{22,20;1,2\}$ $(243,22,1,2)$ $\text{Berlekamp-van Lint-Seidel graph}$ $243$ $\{110,72;1,60\}$ $(243,110,37,60)$ $\text{Delsarte graph}$ $275$ $\{112,81;1,56\}$ $(275,112,30,56)$ $\text{McLaughlin graph}$ $378$ $\{177,80;1,36\}$ $(378,117,36,36)$ $O_7(3) \text{ graph}$ $416$ $\{100,63;1,20\}$ $(416,100,36,20)$ $\mathrm{G}_2(4)\text{ graph}$ $651$ $\{90,56;1,9\}$ $(651,90,33,9)$ $\text{Grassmann graph }J_2(6,2)$ $672$ $\{495,128;1,360\}$ $(672,491,366,360)$ $\text{Distance-2 graph of Moscow-Soicher graph}$ $672$ $\{176,135;1,48\}$ $(672,176,40,48)$ $U_6(2) \text{ graph}$ $729$ $\{112,110;1,20\}$ $(729,112,1,20)$ $\text{Games graph}$ $1600$ $\{351,256;1,72\}$ $(1600,351,94,72)$ $\text{SRG(1600,351,94,72) from Tits group } \phantom{.}^2 F_4(2)'$ $1782$ $\{416,135;1,96\}$ $(1782,416,100,96)$ $\text{Suzuki graph}$

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Last updated: 20 March 2019