有限Jaco图$J_n(1), n \in \Bbb N$的特征
Characteristics of Finite Jaco Graphs, $J_n(1), n \in \Bbb N$
摘要：
我们引入了一族有限有向图（1阶）的概念，它们是从一个无限有向图（1阶）导出的有向图，称为1-根有向图。1-根有向图有四个基本性质：$V(J_\infty(1)) = \{v_i|i \in \Bbb N\}$，并且如果$v_j$是边（弧）的头部，则尾部总是顶点$v_i, i<j$，并且如果$v_k$，对于最小的$k \in \Bbb N$是尾部顶点，则所有顶点$v_\ell, k< \ell <j$是$v_j$的弧的尾部，并且最后，顶点$k$的度是$d(v_k) = k.$有限有向图族是通过去掉所有顶点而限制为$n \in \Bbb N$顶点的图因此，$v_t, t> n.$，我们通常有$d(v_i) \leq i$。我们提出了一个有趣的Fibonaccian-Zeckendorf结果，并提出了Fisher算法表的特定值的兴趣。这是一篇介绍性论文，鼓励探索性研究。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
