# How many vertices for non-isomorphic graphs?

I started drawing planar, cubic, bipartite graphs consisting of faces with $4$ or $6$ vertices only. I found that six $4$-faces are sufficient to do that. The smallest graph is a planar drawing of the cube.

How many vertices or $6$-faces are necessary to get two non-isomorphic graphs?

• Your question is a little confusing. Are you asking for the smallest (in terms of vertices) pair of planar cubic graphs with 6-sided faces? – gilleain Jul 20 '15 at 12:49
• @gilleain yes; 6 4-sided and x 6-sided faces... – draks ... Jul 20 '15 at 14:17