Presenters: Jonathan Mousley, College of Science, Mathematics and Statistics
Authors: Manuel A. Santana, LeRoy B. Beasley, David E. Brown
Faculty Advisors: LeRoy Beasley, College of Science, Mathematics and Statistics
Institution: Utah State University
This presentation is about graphs (the vertex-edge kind, not the y = f(x) kind). A graph is a mathematical object that represents objects and some relationship among them; the objects are represented by vertices and the relationships are represented by the edges. Graphs have applications in just about every field imaginable, including artificial intelligence, social network theory, and parallel computing theory. A directed graph is a type of graph used to represent relationships that are one-sided or not symmetric. We discuss a graph labelling scheme on directed graphs introduced by LeRoy Beasley called a (2,3)-cordial labelling. In such a labelling, the vertex set of a directed graph is partitioned into two equally sized subsets by labelling half of vertices 0 and the other half 1; edges of the directed graph receive a label according to their direction and affiliated vertex labels such that the edge set is partitioned into three equally sized subsets in accord with whether their labels are 1, 0, or -1. Although not every directed graph can be labeled in accord with the (2,3)-cordial scheme, we discuss properties that indicate when a directed graph can be so labeled as well as applications of (2,3)-cordial labelling. In particular, we present results on the existence of (2,3)-cordial labelings on oriented hypercubes, trees, and tournaments.