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Mathematics

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East Tennessee State University

Theses/Dissertations

2015

Graph theory

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On Properties Of RW-Regular Graphs, Franklina Samani Dec 2015

On Properties Of RW-Regular Graphs, Franklina Samani

Electronic Theses and Dissertations

If every vertex in a graph G has the same degree, then the graph is called a regular graph. That is, if deg(v) = r for all vertices in the graph, then it is denoted as an r-regular graph. A graph G is said to be vertex-weighted if all of the vertices are assigned weights. A generalized definition for degree regularity for vertex-weighted graphs can be stated as follows: A vertex-weighted graph is said to be rw-regular if the sum of the weights in the neighborhood of every vertex is rw. If all vertices are assigned …


The Apprentices' Tower Of Hanoi, Cory Bh Ball May 2015

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.