Distance-regular graphs of valency 4

No. of verticesGraphIntersection Array
6Octahedron $J(4,2)$$\{4,1;1,4\}$
9Paley graph $P_9 \cong H(2,3)$$\{4,2;1,2\}$
10$K_{5,5}-I$$\{4,3,1;1,3,4\}$
14Distance-3 graph of Heawood graph$\{4,3,2;1,2,4\}$
15Line graph of Petersen graph$\{4,2,1;1,1,4\}$
164-cube $Q_4 \cong H(4,2)$$\{4,3,2,1;1,2,3,4\}$
21Line graph of Heawood graph$\{4,2,2;1,1,2\}$
26Incidence graph of $PG(2,3)$$\{4,3,3;1,1,4\}$
32Incidence graph of $AG(2,4)$ minus a parallel class$\{4,3,3,1;1,1,3,4\}$
35Odd graph $O_4$$\{4,3,3;1,1,2\}$
45Line graph of Tutte's 8-cage$\{4,3,3;1,1,2\}$
70Doubled Odd Graph $D(O_4)$$\{4,3,3,2,2,1,1;1,1,2,2,3,3,4\}$
80Incidence graph of $GQ(3,3)$$\{4,3,3,3;1,1,1,4\}$
189Line graph of Tutte's 12-cage$\{4,2,2,2,2,2;1,1,1,1,1,2\}$
728Incidence graph of $GH(3,3)$$\{4,3,3,3,3,3;1,1,1,1,1,4\}$

Back to: Graphs by valency
Last updated: 21 February 2017