TITLE: Table of planar connected graphs
QUESTION [6 upvotes]: For the other day I need to use the table of planar connected graph with few vertex. In the wolfram's mathworld , they listed only the graph with $4$ vertex.
Does anyone knows webpages or pdf on the web which carries the table of planar connected graph with up to $10$ edges?

REPLY [11 votes]: A lot depends on what the question means, in particular are the graphs simple, and is equivalence defined by embedding-preserving isomorphism or all graph isomorphisms.
For simple graphs up to general isomorphism, see my page for files up to 11 vertices. 
For simple graphs up to embedding-preserving isomorphism, use plantri to make them.  The command for $n$ vertices is "plantri -pc1m1 $n$", or "plantri -opc1m1 $n$" if mirror-image doesn't count as isomorphism. (At first, add "-u" to just count rather than output.) Tables up to 14 vertices are in this paper, Table 22.