What's the name of a tree that looks like the below?
I've provided a few iterations $d = 0,1, \dotsc$, because it looks sort of fractal. The
0's are nodes, and the lines, edges.
0 | 0-0-0 | 0
$d = 2$
0 | 0 0-0-0 0 | | | 0-0----0----0-0 | | | 0 0-0-0 0 | 0
I was thinking of calling them "lattice trees", but after a bit of Googling, it looks like these might be called "star-like" trees, but if anyone could give a reference or a confirmation that would be nice.
The way I've constructed them is by setting the length of the maximum path in the graph to be $2d$ and then tried to have as many vertices as possible.