  We introduce the concept of a family of finite directed graphs (order 1)
which are directed graphs derived from an infinite directed graph (order 1),
called the 1-root digraph. The 1-root digraph has four fundamental properties
which are; $V(J_\infty(1)) = \{v_i|i \in \Bbb N\}$ and, if $v_j$ is the head of
an edge (arc) then the tail is always a vertex $v_i, i<j$ and, if $v_k$, for
smallest $k \in \Bbb N$ is a tail vertex then all vertices $v_\ell, k< \ell <j$
are tails of arcs to $v_j$ and finally, the degree of vertex $k$ is $d(v_k) =
k.$ The family of finite directed graphs are those limited to $n \in \Bbb N$
vertices by lobbing off all vertices (and edges arcing to vertices) $v_t, t>
n.$ Hence, trivially we have $d(v_i) \leq i$ for $i \in \Bbb N$. We present an
interesting Fibonaccian-Zeckendorf result and present the Fisher Algorithm to
table particular values of interest. It is meant to be an introductory paper to
encourage exploratory research.
