Special Trees

Special trees are easy to generate, as they can be built from several smaller well defined graphs. Recall that a tree $\mathit{Line}(n)$ is a path of length $n-1$, and that $\mathit{Special}(k,t)$ is a graph ``obtained from $k$ copies of paths of length $t$, by making one end of every path adjacent to an additional vertex $z$.'' Then $\mathit{Special}(k,t)$ can be created from the union of a single vertex, and $k$ copies of $\mathit{Line}(t+1)$ (which we denote as $L_1, L_2, \ldots, L_k$) with some adjacency operations.