Graph Theory - Duality of Non Planar Graphs

Question

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?

non-planar graphs don't have faces? – JMP Mar 16 '17 at 08:34 — JMP, Mar 16 '17 at 08:34

score 1 · Answer 1 · edited Apr 13 '17 at 12:19

1

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.

edited Apr 13 '17 at 12:19

Community

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answered Mar 16 '17 at 10:24

Smylic

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Graph Theory - Duality of Non Planar Graphs

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