Pinnacles on Graphs

Mr. Stephen Lasinis
Undergraduate
University of Wisconsin – Milwaukee

We consider graphs that are simple, finite, connected, and undirected, and a bijective labeling on the vertices of the graph with the integers 1, 2, …, n where n is the number of vertices. Whenever a label on a vertex is larger than the label of all of its neighbors, then we say it is a pinnacle. In this talk, we explore pinnacle sets and enumerate labelings that have specific pinnacle sets. We present results on various graph families including complete graphs and star graphs. We also explore the method used to enumerate these labelings algorithmically. This talk is meant to be an accessible introduction to the research area of generalizing pinnacles on graphs.