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Timeline for Table of planar connected graphs

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May 10, 2015 at 2:38 comment added this_is_an_apple >there is an infinite number of graphs $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ To avoid the situation, I wrote "10 edges" in the question above.
May 9, 2015 at 17:38 comment added Noam Zeilberger @this_is_an_apple such illustrated tables are included in the atlas by Jackson and Visentin I referenced above. Since you are considering planar graphs with multiple edges up to embedding-preserving isomorphism, it sounds like the objects you are interested in are precisely what are known as "planar maps".
May 9, 2015 at 14:06 comment added Oliver Krüger @this_is_an_apple If you allow multiple edges there is an infinite number of graphs even for just 2 vertices, since you can have any number of edges between them (and still be planar).
May 9, 2015 at 13:57 comment added this_is_an_apple What I want to know is the planar graph that allows multiple edges up to embedding-preserving isomorphism, and visually illustrated. Does anybody know the table that illustrate these graphs?
May 9, 2015 at 13:26 history answered Brendan McKay CC BY-SA 3.0