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The Doro graph is a distance-transitive and Distance-Regular Graph on 68 vertices and with valency 12. It is the unique automorphic graph having intersection array ...

The cubitruncated cuboctahedral graph is the skeleton of the cubitruncated cuboctahedron, which is the only uniform polyhedron for which this is the case. It is illustrated ...

A generalized Moore graph is a regular graph of degree r where the counts of vertices at each distance d=0, 1, ... from any vertex are 1, r, r(r-1), r(r-1)^2, r(r-1)^3, ..., ...

The truncated dodecadodecahedral graph is the skeleton of the truncated dodecadodecahedron, which is the only uniform polyhedron for which this is the case. It will be ...

A function f is topologically transitive if, given any two intervals U and V, there is some positive integer k such that f^k(U) intersection V!=emptyset. Vaguely, this means ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

A graph in which each graph edge is replaced by a directed graph edge, also called a digraph. A directed graph having no multiple edges or loops (corresponding to a binary ...

The generalized Petersen graph GP(n,k), also denoted P(n,k) (Biggs 1993, p. 119; Pemmaraju and Skiena 2003, p. 215), for n>=3 and 1<=k<=|_(n-1)/2_| is a connected cubic graph ...

The Sims graph is a distance-transitive graph on 352 vertices (Brouwer et al. 1989, p. 370).

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...