Arc-transitive: A graph X is arc-transitive if its automorphism group acts transitively on the set of arcs of X, that is, on the set of ordered pairs of adjacent vertices.
Cayley graph: A graph X is a Cayley graph on a group G if the automorphism group of X contains a subgroup G acting regularly on the vertices of X (that is, acting transitively and with trivial vertex-stabilizers).
Cubic: A graph is cubic if each of its vertex has valency 3.
Dihedrant: A graph X is called a dihedrant if it is a Cayley graph on a dihedral group.
Girth: The girth of a graph is the minimum length of a cycle in the graph.
GRR (Graphical regular representation): A graph X is a GRR if its automorphism group acts regularly on the set of vertices of X (that is, acting transitively and with trivial vertex stabilizers).
Vertex-transitive: A graph X is vertex-transitive if its automorphism group acts transitively on the set of vertices of X.
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