I'm working on a project for a class and as part of that project I (previously) decided to do the following problem from our textbook, Combinatorics and Graph Theory 2nd ed. by Harris, Hirst, & Mossinghoff.
Find a 4-regular planar graph, and prove that it is unique.
(Now that I'm posting this I will be using a different problem for my project whether I get help on this or not.) The issue I'm having is that I don't really buy this. "4-regular" means all vertices have degree 4. A "planar" representation of a graph is one where the edges don't intersect (except technically at vertices). Below are two 4-regular planar graphs which do not appear to be the same or even isomorphic. The first one comes from this post and the second one comes from this post.
What's going on? Am I just missing something trivial here?