Graph-Theoretic Ukulele Strumming Patterns

The objective of this paper is to formalize and investigate a graph-theoretic framework concerning specific strumming techniques distinctive to the ukulele, a Hawaiian-Portuguese instrument, widely popular internationally. Two and three stroke patterns are enumerated and sought in the literature of early influential ukulele methods. Their properties and interconnections are analyzed and patterns involving all the introduced strokes types are modeled with the means of Hamiltonian directed cycles, ultimately aiming to create a pedagogically beneficial set of musical scores/technical studies that would be beneficial to instrumentalists. Possible generalizations and developments of the model are introduced at the end.