Looking at the graphs of diheral groups I noticed most have vertices of degree $2$ or $3$. The reason might seem obvious but in mathematics I have learned not to assume anything!
- Is there such a dihedral graph that has vertices of degree $3$?
And what about diheral symmetry in three dimensions? I have found a graph (I am sure there are many) that has vertices of degree $4$:
- Can we walk about the graph using generators just as we can a diheral graph?
Also, I found another graph with vertices of degree $4$:
- Does this have diheral symmetry in three dimensions? And, as before, can we walk about its graph using generators just as we can a diheral graph?