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Full-Text Articles in Other Mathematics

Ultrametrics And Complete Multipartite Graphs, Viktoriia Viktorivna Bilet, Oleksiy Dovgoshey, Yuriy Nikitovich Kononov Jun 2022

Ultrametrics And Complete Multipartite Graphs, Viktoriia Viktorivna Bilet, Oleksiy Dovgoshey, Yuriy Nikitovich Kononov

Theory and Applications of Graphs

Let (X, d) be a semimetric space and let G be a graph. We say that G is the diametrical graph of (X, d) if X is the vertex set of G and the adjacency of vertices x and y is equivalent to the equality diam X = d(x, y). It is shown that a semimetric space (X, d) with diameter d* is ultrametric if the diametrical graph of (X, d ε) with d ε (x, y) = min{d(x, y), ε} is complete multipartite for every ε ∈ (0, d* …


Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier Jan 2019

Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier

Electronic Theses and Dissertations

We explore a relatively new concept in edge-colored graphs called conflict-free connectivity. A conflict-free path is a (edge-) colored path that has an edge with a color that appears only once. Conflict-free connectivity is the maximal number of internally disjoint conflict-free paths between all pairs of vertices in a graph. We also define the c-conflict-free-connection of a graph G. This is the maximum conflict-free connectivity of G over all c-colorings of the edges of G. In this paper we will briefly survey the works related to conflict-free connectivity. In addition, we will use the probabilistic method to achieve a bound …


Combinatorial Game Theory: An Introduction To Tree Topplers, John S. Ryals Jr. Jan 2015

Combinatorial Game Theory: An Introduction To Tree Topplers, John S. Ryals Jr.

Electronic Theses and Dissertations

The purpose of this thesis is to introduce a new game, Tree Topplers, into the field of Combinatorial Game Theory. Before covering the actual material, a brief background of Combinatorial Game Theory is presented, including how to assign advantage values to combinatorial games, as well as information on another, related game known as Domineering. Please note that this document contains color images so please keep that in mind when printing.