A simple n-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers 1 through n such that adjacent vertices have relatively prime labels. We will present previously unknown prime vertex labelings for new families of graphs, all of which are special cases of Seoud and Youssef's conjecture that all unicyclic graphs have a prime labeling.
Dana C. Ernst, Jeff Rushall
Diefenderfer, Nathan; Hastings, Michael; Heath, Levi N.; Prawzinsky, Hannah; Preston, Briahna; White, Emily; and Whittemore, Alyssa
"Prime Vertex Labelings of Families of Unicyclic Graphs,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
1, Article 14.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/14