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

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...

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Bibliographic Details
Published in:arXiv.org 2014-04
Main Authors: Kok, Johan, Fisher, Paul, Wilkens, Bettina, Mabula, Mokhwetha, Mukungunugwa, Vivian
Format: Article
Language:English
Subjects:
Apexes
Graph theory
Graphs
Logic programming
Online Access:Get full text
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Summary: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.
ISSN:2331-8422