distance-regular graph
a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k
Sylvester graph
5-regular graph with 36 vertices and 90 edges
octahedral graph
polyhedral graph of the octahedron, with 6 vertices and 12 edges
Desargues graph
highly symmetric graph with 20 vertices and 30 edges
Coxeter graph
cubic distance-regular graph with 28 vertices and 42 edges
dodecahedral graph
polyhedral graph of the dodecahedron, with 20 vertices and 30 edges
distance-transitive graph
graph where any two nodes of equal distance are isomorphic
halved cube graph
graph whose vertices are binary numbers with even numbers of nonzero bits and whose edges connect closest pairs in Hamming distance
Pappus graph
graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration
Wells graph
5-regular graph with 32 vertices and 80 edges
hypercube graph
graphs formed by a hypercube's edges and vertices
odd graph
family of symmetric graphs which generalize the Petersen graph
strongly regular graph
graph in which the number of shared neighbors of two vertices depends only on whether they are adjacent
Suzuki graph
strongly regular graph with 1782 vertices and 370656 edges
Hamming graph
cartesian product of isomorphic complete graphs
icosahedral graph
polyhedral graph of the icosahedron, with 12 vertices and 30 edges