In my lectures I have the definition of dual graphs linked to planar graphs. Is there a way to prove (or any prove already made) that I can't get a dual graph from a non-planar graph?
2026-03-27 03:49:51.1774583391
Graph Theory - Duality of Non Planar Graphs
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You can embed any finite non-planar graph into surface of higher genus (and plane is genus-0 surface) and find its dual graph using this embedding. So restriction of duality definition by planar graph only is like getting square root of non-negative numbers only, it makes sense just to simplify studying.
Edit. You can read more precise answer here.