Consider a point in a plane with a red green and blue line coming out of it. There are two ways the lines can be ordered, clockwise and anti-clockwise.
Similarly for 4 lines in 3D coming from a point, there are two inequivalent orientations.
Is there a name for graphs in which we take into account this orientation.
For example consider two points with three lines connecting them. There would be 2 inequvalient of these graphs, depending on whether both orientations are the same or different.
These types of graphs are useful for representing anti-symmetric tensors. But do they have a special name?
This is called a 'Combinatorial Embedding' (or Rotation System) of a graph. So it's not so much a particular 'type' of graph, I suppose, but additional structure for an existing graph.
Although this structure is often used for 2D embeddings - for planar graphs - I believe it generalises to higher dimensions. As an aside, for 3D this is the concept of 'chirality' in chemistry where the orientation of bonds around an atom is important for the structure of a molecule.