$\text{Distance-regular graphs on up to 50 vertices}$

$``N=k" \text{denotes that there are } k \text{ non-isomorphic examples of such graphs.}$
GraphNo. of verticesDiameter
$\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{Incidence graph of }PG(2,4)$$42$$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$

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Last updated: 14 August 2018