arXiv subjects

Bettina Wilkens

Publications and source records attributed to Bettina Wilkens.

2 recordsLinked to original sources

arXiv2014

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 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.

math.CO↗

arXiv2014

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

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.

math.CO↗