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Discrete Mathematics and Combinatorics Commons™
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Full-Text Articles in Discrete Mathematics and Combinatorics
Jumping Frogs On Cyclic Graphs, Jake Mitchell
Jumping Frogs On Cyclic Graphs, Jake Mitchell
Honors College Theses
From the traditional game of Solitaire to modern video games like Candy Crush and Five Nights at Freddy’s, single-player games have captivated audiences for gener- ations. We investigate a lesser-known single-player game, the Jumping Frogs problem, on various classes of simple graphs, a graph with no multiple edges or looped ver- tices. We determine whether frogs can be stacked together on one vertex of a given graph. In a graph with k vertices and one frog on each vertex, the frogs must make legal jumps to form a stack of k frogs. The problem is known to be solvable on …
Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim
Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim
Electronic Theses, Projects, and Dissertations
Self-assembly is the process of a collection of components combining to form an organized structure without external direction. DNA self-assembly uses multi-armed DNA molecules as the component building blocks. It is desirable to minimize the material used and to minimize genetic waste in the assembly process. We will be using graph theory as a tool to find optimal solutions to problems in DNA self-assembly. The goal of this research is to develop a method or algorithm that will produce optimal tile sets which will self-assemble into a target DNA complex. We will minimize the number of tile and bond-edge types …