Given a cubic planar graph, if I "walk" on one edge to get to a vertex, it it possible to know which of the other two edges is the left edge and which one is the right edge? Am I forced to draw the graph on paper, without edge crossing, and visually identify left and right edges?
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My comment as an answer so it can be accepted:
The answer is no: This can't be possible, since you could draw the mirror image instead, and then left and right edges would be swapped, so they can't be determined by the abstract graph alone.