List of $4$-valent planar graphs

Question

May I know where I can find a complete list of $4$-valent planer graphs with $n$ vertices for relatively small value of $n$?

Answer 1

If your value of $n$ is small, but not so small that you want to go through a list of knots and links by and, an alternative is plantri: http://users.cecs.anu.edu.au/~bdm/plantri/.

This is a C program that will generate a list of planar graphs with certain properties, depending on the input. In your case, supposing you want graphs on $12$ vertices, you could use

plantri -p -m4 -c1 -e24 12

where -p asks for general planar simple graphs, -m4 asks for graphs with minimum degree $4$, -c1 asks for graphs with minimum connectivity $1$ (connected graphs), -e24 asks for graphs with $24$ edges (together with the minimum degree condition, this implies that the graph is $4$-regular), and 12 asks for $12$-vertex graphs.

(In general, for $n$-vertex graphs, you will want the -e parameter to be $2n$.)