A Study on Linear Jaco Graphs
Johan Kok, C Susanth, Sunny Joseph Kalayathankal · Journal of Informatics and Mathematical Sciences · 2015
We introduce the concept of a family of nite directed graphs (positive integer order, $f(x) =mx+c$; $x, m \in \mathbb{N}$ and $c \in \mathbb{N}_0$) which are directed graphs derived from an innite directed graph called the $f(x)$-root digraph. The $f(x)$-root digraph has four fundamental properties which are; $V (J_\infty(f(x))) = \{v_i : i \in \mathbb{N}\}$ and, if $v_j$ is the head of an arc then the tail is always a vertex $v_i$, $i n$. Hence, trivially we have $d(v_i) mi + c$ for $i \in \mathbb{N}$. It is meant to be an introductory paper to encourage further research.