Competition Graphs

Abstract

Competition graphs were originally created in 1968 by Biologist Joel Cohen. In this paper we discuss four things. First, the use of linear algebra is considered with connection to competition graphs. Second, we generalize the idea of the competition graph into the m-step competition graph, and characterize P_{n} as an m-step competition graph. Third, we begin to characterize disjoint unions of graphs as m-step competition graphs. And last, we explore what happens if we treat m-step competition graphs as an infinite sequence, called a competition sequence.