Stephen Lasinis, “Pinnacles on Graphs”
Mentor: Pamela Harris, Mathematical Sciences
Poster #176

Given a simple connected graph G with n vertices and a bijective labeling of the vertices using the integers [n] = {1, 2, . . . , n}, we say j ∈ [n] is a pinnacle of G if the label j on vertex v is larger than the labels of all the vertices neighboring v. Given a subset S ⊆ [n], if there exists a labeling of G such that S is the set of all pinnacles, then we say that S is an admissible pinnacle set of G. We explore the properties of pinnacle sets as well as how to enumerate how many labelings of G result in particular pinnacle sets. We present results on certain graph families including complete graphs, star graphs, and cycle graphs.