Fortunately we know the following facts that if $G$ is a planar graph with minimum degree 5 then it has at least 12 vertices.
I consider 5-regular planar graph. We find a graph with 12 vertices that satisfies the conditions. By doing limited copy of following graph, we can get more 5 regular planar graphs. But what I mean is whether it is possible to find more connected 5 regular planar graphs with more than 12 vertices.
Is there any literature on this issue ? Any suggestions are valuable.
This question is related to the question I just asked on the forum.
I see this link seems to be related to my problem.