(graph theory) A regular graph of degree d and diameter k whose number of vertices equals the upper bound 1+d∑ᵢ₌₀ᵏ⁻¹(d-1)ⁱ.

plural of graph hole

plural of graph antihole

plural of graph state

(graph theory) A graph derived from a given plane graph such that this derived graph has a vertex corresponding to each edge of the given graph, and such that for every “angle” (consecutive trio of edge, vertex, edge) along the border of a face of the given graph there is a corresponding edge which connects the vertices corresponding to the two edges that are part of that “angle”.

(graph theory) A graph derived from some plane graph in such a way that the derived graph has a vertex corresponding to each face of the given graph, an edge corresponding to each edge of the given graph that is shared by a pair of distinct faces, and a self-loop for each edge of the given graph that is a border of the same face on both of its sides.

(graph theory) An embedding of a planar graph in a plane.

(graph theory) A graph which can be embedded in a plane in such a way that its edges only intersect at vertices, i.e., they do not cross each other.

(graph theory) A 3-regular graph; i.e., a graph whose every vertex has degree three.

(graph theory) A graph whose vertices all have the same degree.