An $l$ long $k$-star is a graph with centeral vertex $o$ which is connected to $k$ line graphs of length $l$.
For example a 2-long 3-star looks like:
x1-x1-O-x2-x2 | x3-x3
$o$ is the central node, $x1,x2,x3$ are the three line-graphs connected to $o$.
Rigorously speaking, an $\ell$-long $k$ star is composed of:
- $k$ line graphs $l_1,l_2,\dots,l_k$ each with $\ell$ vertices
- centeral vertex $o$
- $k$ edges $(o,l_1),(o,l_2),\dots,(o,l_k)$
Is there a "standard" name for such a graph family?