Lesley W. Wiglesworth’s research while affiliated with Danville Community College and other places

A graph labeling assigns integers to the vertices or edges (or both) of a graph, subject to certain conditions. Labelings were first studied in the late 1960s, making them a relatively new area of mathematics to explore. There are hundreds of different types of labelings, many of which are motivated by circuit design, coding theory, and communication networks. In this chapter, we introduce the reader to prime labelings, a labeling of the vertices in such a way that the labels of adjacent vertices are relatively prime. We also introduce several variations of prime labelings while guiding the reader through examples and existing research. We present the reader with several research questions for each variation, several of which have never been explored, thus allowing the reader to make progress on new problems.

As studies repeatedly show the benefits of students participating in undergraduate research, off-campus research opportunities have become increasingly competitive. In order to provide our students with research experiences, students from Murray State University and Centre College engaged in a year-long cross-institutional undergraduate research experience. In this paper, we summarize our experience and provide some useful perspectives in mentoring students in cross-institutional undergraduate research. We present effective methods for improving distance collaboration and strategies for eliciting the best research from students.

A prime labeling of a graph G with n vertices is a labeling of the vertices with distinct integers from the set {1, 2,. .. , n} such that the labels of any two adjacent vertices are relatively prime. In this paper, we introduce a snake graph, the fused union of identical cycles, and define a consecutive snake prime labeling for this new family of graphs. We characterize some snake graphs that have a consecutive snake prime labeling and then consider a variation of this labeling.