Ed et Al, I won't post the answer, but see Guy & Harary, On the M"obius ladders [also available in Hungarian!] MR 37 #98, #2627 R. On Wed, 28 Feb 2007, Ed Pegg Jr wrote:
Crossing number 1 -- Utility graph -- 6 vertices Crossing number 2 -- Petersen graph -- 10 vertices Crossing number 3 -- Heawood graph -- 14 vertices
Crossing number 8 -- Mcgee graph -- 24 vertices.
What are the simplest cubic graphs with crossing number 4-7 ?
As a warm-up exercise to how tricky this problem is, show that a even n-gon with opposite corners connected has crossing number 1. (No need to post a proof here.)
--Ed Pegg Jr
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