I have the following 12-node planar undirected graph:
Can this particular graph be said to belong to any defined family of graphs? Is it perhaps part of a discrete continuum of graphs?
It is (obviously) not the complete $K_{12}$, and it is not regular as 4 and 8 vertices have degree 4 and 3, respectively. The only thing I can see structurally, is that it seems to be a combination of three kinds of cycle graphs: $3 \times C_3$, $1 \times C_4$, and $1 \times C_6$.
Can anything interesting be said about it? Rotational symmetry?
I add tags on algebraic and spectral graph theory, since these fields are also of interest. Anything goes.
PS: No, this is not homework. Just tired of looking at this drawing :-)