Competition Graphs of Jaco Graphs and the Introduction of the Grog Number of a Simple Connected Graph
Johan Kok, Susanth C, Sunny Joseph Kalayathankal

TL;DR
This paper characterizes the competition graph of Jaco graphs and introduces the grog number, a new measure of predator-prey strategy efficiency in ecological web models, along with open research problems.
Contribution
It provides a formula for the competition graph of Jaco graphs and introduces the novel grog number to quantify predator-prey strategy efficiency.
Findings
Explicit formula for the competition graph of Jaco graphs.
Introduction of the grog number as a new ecological measure.
Poses open problems for future research.
Abstract
Let be a simple connected directed graph on vertices and let be a non-empty subset of and denote the undirected subgraph induced by by, We show that the \emph{competition graph} of the Jaco graph denoted by is given by:\\ \\ \\ \\ Further to the above, the concept of the \emph{grog number} of a simple connected directed graph on vertices as well as the general \emph{grog number} of the underlying graph , will be introduced. The \emph{grog number} measures the efficiency of an \emph{optimal predator-prey strategy} if the simple directed graph models an…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems
