$``N=k" \text{denotes that there are } k \text{ non-isomorphic examples of such graphs.}$
| Graph | No. of vertices | Diameter |
| $\text{Octahedron }J(4,2)$ | $6$ | $2$ |
| $\text{Cube }Q_3 \cong K_{4,4}-I \cong H(3,2)$ | $8$ | $3$ |
| $\text{Paley graph }P_9 \cong H(2,3)$ | $9$ | $2$ |
| $\text{Petersen graph }O_3 = K(5,2)$ | $10$ | $2$ |
| $J(5,2)$ | $10$ | $2$ |
| $K_{5,5}-I$ | $10$ | $3$ |
| $\text{Icosahedron}$ | $12$ | $3$ |
| $K_{6,6}-I$ | $12$ | $3$ |
| $\text{Paley graph }P_{13}$ | $13$ | $2$ |
| $\text{Heawood graph (Incidence graph of }PG(2,2)\text{)}$ | $14$ | $3$ |
| $\text{Distance-3 graph of Heawood graph}$ | $14$ | $3$ |
| $K_{7,7}-I$ | $14$ | $3$ |
| $\text{Line graph of Petersen graph}$ | $15$ | $3$ |
| $K(6,2)$ | $15$ | $2$ |
| $J(6,2)$ | $15$ | $2$ |
| $\text{4-cube }Q_4 \cong H(4,2)$ | $16$ | $4$ |
| $H(2,4)$ | $16$ | $2$ |
| $\text{Complement of }H(2,4)$ | $16$ | $2$ |
| $\text{Shrikhande graph}$ | $16$ | $2$ |
| $\text{Complement of Shrikhande graph}$ | $16$ | $2$ |
| $\text{Clebsch graph}$ | $16$ | $2$ |
| $\text{Complement of Clebsch graph}$ | $16$ | $2$ |
| $K_{8,8}-I$ | $16$ | $2$ |
| $\text{Paley graph }P_{17}$ | $17$ | $2$ |
| $\text{Pappus graph}$ | $18$ | $4$ |
| $K_{9,9}-I$ | $18$ | $3$ |
| $\text{Dodecahedron}$ | $20$ | $5$ |
| $\text{Desargues graph }D(O_3)$ | $20$ | $5$ |
| $J(6,3)$ | $20$ | $3$ |
| $K_{10,10}-I$ | $20$ | $3$ |
| $\text{Line graph of Heawood graph}$ | $21$ | $3$ |
| $J(7,2)$ | $21$ | $2$ |
| $K(7,2)$ | $21$ | $2$ |
| $\text{Incidence graph of biplane on 11 points}$ | $22$ | $3$ |
| $\text{Incidence graph of }(11,6,3)\text{-design}$ | $22$ | $3$ |
| $K_{11,11}-I$ | $22$ | $3$ |
| $\text{Klein graph}$ | $24$ | $3$ |
| $K_{12,12}-I$ | $24$ | $3$ |
| $H(2,5)$ | $25$ | $2$ |
| $\text{Paley graph }P_{25}$ | $25$ | $2$ |
| $\text{Paulus graphs, SRG(25,12,5,6) }(N=14, \text{ 7 pairs)}$ | $25$ | $2$ |
| $\text{Complement of }H(2,5)$ | $25$ | $2$ |
| $\text{Paulus graphs, SRG(26,10,3,4) }(N=10)$ | $26$ | $2$ |
| $\text{Complements of Paulus graphs, SRG(26,15,8,9) }(N=10)$ | $26$ | $2$ |
| $\text{Incidence graph of PG(2,3)}$ | $26$ | $3$ |
| $\text{Incidence graph of }(13,9,3)\text{-design}$ | $26$ | $3$ |
| $K_{13,13}-I$ | $26$ | $3$ |
| $\text{Complements of Paulus graphs, srg(26,15,8,9) }(N=10)$ | $26$ | $2$ |
| $H(3,3)$ | $27$ | $3$ |
| $GQ(2,4)\text{ minus spread }(N=2)$ | $27$ | $3$ |
| $\text{Complement of Schl}\ddot{a}\text{fli graph}$ | $27$ | $2$ |
| $\text{Schl}\ddot{a}\text{fli graph}$ | $27$ | $2$ |
| $\text{Coxeter graph}$ | $28$ | $4$ |
| $J(8,2)$ | $28$ | $2$ |
| $\text{Chang graphs }(N=3)$ | $28$ | $2$ |
| $\text{Taylor graph from }P_{13}$ | $28$ | $3$ |
| $K_{14,14}-I$ | $28$ | $3$ |
| $K(8,2)$ | $28$ | $2$ |
| $\text{Complements of Chang graphs }(N=3)$ | $28$ | $2$ |
| $\text{Paley graph }P_{29}$ | $29$ | $2$ |
| $\text{Other srg(29,14,6,7) }(N=40, 20 \text{ pairs)}$ | $29$ | $2$ |
| $\text{Tutte's 8-cage}$ | $30$ | $4$ |
| $\text{Incidence graph of }PG(3,2)$ | $30$ | $3$ |
| $\text{Incidence graphs of Hadamard (15,7,3)-designs }(N=4)$ | $30$ | $3$ |
| $\text{Incidence graph of complement of }PG(3,2)$ | $30$ | $3$ |
| $\text{Incidence graphs of }(15,8,4)\text{-designs }(N=4)$ | $30$ | $3$ |
| $K_{15,15}-I$ | $30$ | $3$ |
| $\text{Incidence graph of }AG(2,4) \text{ minus a parallel class}$ | $32$ | $4$ |
| $\text{5-cube }Q_5 \cong H(5,2)$ | $32$ | $5$ |
| $\text{Armanios-Wells graph}$ | $32$ | $4$ |
| $\text{Folded 6-cube}$ | $32$ | $3$ |
| $\text{Incidence graphs of biplanes on 16 points }(N=3)$ | $32$ | $3$ |
| $\text{Incidence graphs of }(16,10,6)\text{-designs }(N=3)$ | $32$ | $3$ |
| $\text{Hadamard graph on 32 vertices}$ | $32$ | $4$ |
| $\text{Taylor graph from }J(6,2) \cong \text{ Halved 6-cube}$ | $32$ | $3$ |
| $\text{Taylor graph from }K(6,2)$ | $32$ | $3$ |
| $K_{16,16}-I$ | $32$ | $3$ |
| $K_{17,17}-I$ | $34$ | $3$ |
| $\text{Grassmann graph }J_2(4,2)$ | $35$ | $2$ |
| $\text{Odd graph }O_4$ | $35$ | $3$ |
| $J(7,3)$ | $35$ | $3$ |
| $\text{Sylvester graph}$ | $36$ | $3$ |
| $\text{Hexacode graph}$ | $36$ | $4$ |
| $H(2,6)$ | $36$ | $2$ |
| $\text{Point graphs of }GQ(3,3) \text{ and its dual}$ | $40$ | $2$ |
| $\text{Coolsaet-Degraer 3-cover of }K_{14}$ | $42$ | $3$ |
| $\text{Incidence graph of }PG(2,4)$ | $42$ | $3$ |
| $\text{Symplectic 3-cover of }K_{14}$ | $42$ | $3$ |
| $2^{\text{nd}} \text{ subconstituent of Hoffman-Singleton graph}$ | $42$ | $3$ |
| $\text{Line graph of Tutte's 8-cage}$ | $45$ | $4$ |
| $\text{Halved Foster graph}$ | $45$ | $4$ |
| $\text{Point graph of }GQ(4,2)$ | $45$ | $2$ |
| $\text{Hadamard graph on 48 vertices}$ | $48$ | $4$ |
| $H(2,7)$ | $49$ | $2$ |
| $\text{Incidence graph of } AG(2,5) \text{ minus a parallel class}$ | $50$ | $4$ |
| $\text{Hoffman-Singleton graph}$ | $50$ | $2$ |
| $\text{Complement of Hoffman-Singleton graph}$ | $50$ | $2$ |