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Discrete Mathematics and Combinatorics Commons™
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Full-Text Articles in Discrete Mathematics and Combinatorics
Roman Domination Cover Rubbling, Nicholas Carney
Roman Domination Cover Rubbling, Nicholas Carney
Electronic Theses and Dissertations
In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for paths and give an upper bound for the …
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Electronic Theses and Dissertations
There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of different musical notes, each of which has different sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.
Vertex Weighted Spectral Clustering, Mohammad Masum
Vertex Weighted Spectral Clustering, Mohammad Masum
Electronic Theses and Dissertations
Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to …
The Apprentices' Tower Of Hanoi, Cory Bh Ball
The Apprentices' Tower Of Hanoi, Cory Bh Ball
Electronic Theses and Dissertations
The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.