Special Trees

Later we concern ourselves with the construction and labeling of special graphs. So, while they do not influence representation at this stage, we need to be able to refer to the `special' trees unambiguously later. Our special trees are those

``obtained from $k$ copies of paths of length $t$, by making one end of every path adjacent to an additional vertex $z$. thus the input to the program is comprised of two integers: $k$ and $t$.''

We will denote a tree of this form as $\mathit{Special}(k,t)$. Two examples are shown in Figure 1. We define a predicate $\mathit{Special?}(G)$ which is true if and only if $G$ is a special tree.

Figure: $\mathit{Special}(3,2)$ and $\mathit{Special}(5,4)$