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arXiv · 1404.1714

Characteristics of Jaco Graphs, $J_\infty(a), a \in \Bbb N$

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 a) which are directed graphs derived from an infinite directed graph (order a), called the a-root digraph. The a-root digraph has four fundamental properties which are; $V(J_\infty(a)) = \{v_i|i \in \Bbb N\}$ 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 $d(v_i) \leq ai$ for $i \in \Bbb N.$ We present an interesting Lucassian-Zeckendorf result and other general results 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. 2014-04-07. Characteristics of Jaco Graphs, $J_\infty(a), a \in \Bbb N$. https://arxiv.org/abs/1404.1714

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