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arXiv · 1404.0484

Characteristics of Finite Jaco Graphs, $J_n(1), n \in \Bbb N$

Johan Kok·Paul Fisher·Bettina Wilkens·Mokhwetha Mabula·Vivian Mukungunugwa
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Abstract

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 $v_i, i n.$ 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.

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Johan Kok, Paul Fisher, Bettina Wilkens, Mokhwetha Mabula, Vivian Mukungunugwa. 2014-04-02. Characteristics of Finite Jaco Graphs, $J_n(1), n \in \Bbb N$. https://arxiv.org/abs/1404.0484

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