Project Description
Graph labeling is a subfield of graph theory involving the assignment of labels to the vertices or edges in a graph such that certain properties of the graph can be studied or analyzed. The history of graph labeling dates back to the early 1900s in the form of graph coloring with the advent of the four-color problem. During the 1950s and 60s, electronic computers gave a significant boost to graph labeling allowing for the efficient computation of various graph parameters. In this project we look at specific type off graph labeling which describes a set of pinnacles, labels whose value is larger than all of the labels in neighboring vertices, these are called pinnacles of a graph. The project will enumerate distinct labeling of certain families of graphs which specify a set of pinnacle values. This work expands on past work of mine on peaks on graphs. The methodology is twofold: algorithmic and theoretical. By creating algorithms, we will be able to conjecture formulas for the number of graph labeling with given pinnacle sets, based on those conjectures we then apply theoretical/mathematical arguments/proofs to establish their validity.
Tasks and Responsibilites
write algorithms to enumerate graph labeling with certain pinnacle sets, write results in a shared overleaf file which allows us to write mathematical text and work to prove the results while provided feedback on the arguments and directions for ways to expand the findings. Weekly meetings are expected so as to report that week's progress and updating the file with algorithms and results weekly to show progress in the research process. Expectations also include creating a poster and a slide deck for presenting the findings of this research with the aim of giving presentations at local conferences.