Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
-
- University of New Mexico (5)
- East Tennessee State University (4)
- Louisiana Tech University (2)
- Arcadia University (1)
- California State University, San Bernardino (1)
-
- Georgia Southern University (1)
- Macalester College (1)
- Marshall University (1)
- Portland State University (1)
- Rose-Hulman Institute of Technology (1)
- St. John Fisher University (1)
- University of Arkansas, Fayetteville (1)
- University of Denver (1)
- Virginia Commonwealth University (1)
- Western University (1)
- Publication Year
- Publication
-
- Electronic Theses and Dissertations (6)
- Branch Mathematics and Statistics Faculty and Staff Publications (5)
- Doctoral Dissertations (2)
- Capstone Showcase (1)
- Electronic Theses, Projects, and Dissertations (1)
-
- Mathematical Sciences Undergraduate Honors Theses (1)
- Mathematics, Statistics, and Computer Science Honors Projects (1)
- Rose-Hulman Undergraduate Mathematics Journal (1)
- Student Research Symposium (1)
- The Review: A Journal of Undergraduate Student Research (1)
- Theses and Dissertations (1)
- Theses, Dissertations and Capstones (1)
- Undergraduate Student Research Internships Conference (1)
- Publication Type
Articles 1 - 23 of 23
Full-Text Articles in Other Mathematics
The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, Yasmin Aguillon, Xingyu Cheng, Spencer Eddins, Pedro Morales
The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, Yasmin Aguillon, Xingyu Cheng, Spencer Eddins, Pedro Morales
Rose-Hulman Undergraduate Mathematics Journal
DNA and other polymer chains in confined spaces behave like closed loops. Arsuaga et al. \cite{AB} introduced the uniform random polygon model in order to better understand such loops in confined spaces using probabilistic and knot theoretical techniques, giving some classification on the mean squared linking number of such loops. Flapan and Kozai \cite{flapan2016linking} extended these techniques to find the mean sum of squared linking numbers for random linear embeddings of complete graphs $K_n$ and found it to have order $\Theta(n(n!))$. We further these ideas by inspecting random piecewise-linear embeddings of complete graphs and give introductory-level summaries of the ideas …
On 2-Primitive Triangle Decompositions Of Cocktail Party Graphs, Ian P. Waddell
On 2-Primitive Triangle Decompositions Of Cocktail Party Graphs, Ian P. Waddell
Theses, Dissertations and Capstones
A decomposition of a graph Γ is a collection C of subgraphs, perhaps nonisomorphic, that partition the edges of Γ. Analogously, consider a group of truck drivers whose non-overlapping routes jointly cover all of the roads between a set of cities; that is, each road is traversed by precisely one driver. In this scenario, the cities are the vertices of the graph, the roads are the edges between vertices, and the drivers’ routes are the subgraphs in the decomposition. Given a graph H, we call C an H-decomposition of Γ if each subgraph in C is isomorphic to …
3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, Rachel Mccann
3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, Rachel Mccann
Mathematical Sciences Undergraduate Honors Theses
The complete 3-uniform hypergraph of order v is denoted as Kv and consists of vertex set V with size v and edge set E, containing all 3-element subsets of V. We consider a 3-uniform hypergraph P7, a path with vertex set {v1, v2, v3, v4, v5, v6, v7} and edge set {{v1, v2, v3}, {v2, v3, v4}, {v4, v5, v6}, {v5, v6 …
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
The Review: A Journal of Undergraduate Student Research
The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …
Local-Global Results On Discrete Structures, Alexander Lewis Stevens
Local-Global Results On Discrete Structures, Alexander Lewis Stevens
Electronic Theses and Dissertations
Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …
Equitable Coloring Of Complete Tripartitle Graphs, Maxwell Vlam, Bailey Orehosky, Dominic Ditizio
Equitable Coloring Of Complete Tripartitle Graphs, Maxwell Vlam, Bailey Orehosky, Dominic Ditizio
Capstone Showcase
In this paper, we prove the Equitable Coloring Conjecture for variations of complete tripartite graphs with graphs K_n,n,n, K_n,n,2n, K_n,n,n+2, and K_n,n+2,n+4.
Categorical Aspects Of Graphs, Jacob D. Ender
Categorical Aspects Of Graphs, Jacob D. Ender
Undergraduate Student Research Internships Conference
In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.
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 …
Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier
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 …
Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K
Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, there by theorising the importance, and giving certain postulates how to safely form ego centric multi networks. Given any subset vertex multigraph we …
A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr
A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr
Doctoral Dissertations
A graph is outer-planar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outer-planar (NOP) if it is edgeless or has an edge whose deletion results in an outer-planar graph. An edge of a non outer-planar graph whose removal results in an outer-planar graph is a vulnerable edge. This dissertation focuses on near outer-planar (NOP) graphs. We describe the class of all such graphs in terms of a finite list of excluded graphs, in a manner similar to the well-known Kuratowski Theorem for planar …
Italian Domination In Complementary Prisms, Haley D. Russell
Italian Domination In Complementary Prisms, Haley D. Russell
Electronic Theses and Dissertations
Let $G$ be any graph and let $\overline{G}$ be its complement. The complementary prism of $G$ is formed from the disjoint union of a graph $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\overline{G}$. An Italian dominating function on a graph $G$ is a function such that $f \, : \, V \to \{ 0,1,2 \}$ and for each vertex $v \in V$ for which $f(v)=0$, it holds that $\sum_{u \in N(v)} f(u) \geq 2$. The weight of an Italian dominating function is the value $f(V)=\sum_{u \in V(G)}f(u)$. …
Subset Vertex Graphs For Social Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Subset Vertex Graphs For Social Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce the notion of subset vertex graph using the vertex set as the subset of the power set P(S), S is assumed in this book to be finite; however it can be finite or infinite. We have defined two types of subset vertex graphs, one is directed and the other one is not directed. The most important fact which must be kept in record is that for a given set of vertices there exists one and only one subset vertex graph be it of type I or type II. Several important and …
Complex Valued Graphs For Soft Computing, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K
Complex Valued Graphs For Soft Computing, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce in a systematic way the notion of complex valued graphs, strong complex valued graphs and complex neutrosophic valued graphs. Several interesting properties are defined, described and developed. Most of the conjectures which are open in case of usual graphs continue to be open problems in case of both complex valued graphs and strong complex valued graphs. We also give some applications of them in soft computing and social networks. At this juncture it is pertinent to keep on record that Dr. Tohru Nitta was the pioneer to use complex valued graphs …
Realizing Tournaments As Models For K-Majority Voting, Gina Marie Cheney
Realizing Tournaments As Models For K-Majority Voting, Gina Marie Cheney
Electronic Theses, Projects, and Dissertations
A k-majority tournament is a directed graph that models a k-majority voting scenario, which is realized by 2k - 1 rankings, called linear orderings, of the vertices in the tournament. Every k-majority voting scenario can be modeled by a tournament, but not every tournament is a model for a k-majority voting scenario. In this thesis we show that all acyclic tournaments can be realized as 2-majority tournaments. Further, we develop methods to realize certain quadratic residue tournaments as k-majority tournaments. Thus, each tournament within these classes of tournaments is a model for a k …
Math And Sudoku: Exploring Sudoku Boards Through Graph Theory, Group Theory, And Combinatorics, Kyle Oddson
Math And Sudoku: Exploring Sudoku Boards Through Graph Theory, Group Theory, And Combinatorics, Kyle Oddson
Student Research Symposium
Encoding Sudoku puzzles as partially colored graphs, we state and prove Akman’s theorem [1] regarding the associated partial chromatic polynomial [5]; we count the 4x4 sudoku boards, in total and fundamentally distinct; we count the diagonally distinct 4x4 sudoku boards; and we classify and enumerate the different structure types of 4x4 boards.
Neighborhood-Restricted Achromatic Colorings Of Graphs, James D. Chandler Sr.
Neighborhood-Restricted Achromatic Colorings Of Graphs, James D. Chandler Sr.
Electronic Theses and Dissertations
A (closed) neighborhood-restricted 2-achromatic-coloring of a graph G is an assignment of colors to the vertices of G such that no more than two colors are assigned in any closed neighborhood. In other words, for every vertex v in G, the vertex v and its neighbors are in at most two different color classes. The 2-achromatic number is defined as the maximum number of colors in any 2-achromatic-coloring of G. We study the 2-achromatic number. In particular, we improve a known upper bound and characterize the extremal graphs for some other known bounds.
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
Theses and Dissertations
An n-dimensional halved cube is a graph whose vertices are the binary strings of length n, where two vertices are adjacent if and only if they differ in exactly two positions. It can be regarded as the graph whose vertex set is one partite set of the n-dimensional hypercube, with an edge joining vertices at hamming distance two. In this thesis we compute the automorphism groups of the halved cubes by embedding them in R n and realizing the automorphism group as a subgroup of GLn(R). As an application we show that a halved cube is a circulant graph if …
Strong Neutrosophic Graphs And Subgraph Topological Subspaces, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilantheral K
Strong Neutrosophic Graphs And Subgraph Topological Subspaces, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilantheral K
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce the notion of strong neutrosophic graphs. They are very different from the usual graphs and neutrosophic graphs. Using these new structures special subgraph topological spaces are defined. Further special lattice graph of subgraphs of these graphs are defined and described. Several interesting properties using subgraphs of a strong neutrosophic graph are obtained. Several open conjectures are proposed. These new class of strong neutrosophic graphs will certainly find applications in NCMs, NRMs and NREs with appropriate modifications.
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.
Neutrosophic Graphs: A New Dimension To Graph Theory, Florentin Smarandache, Wb. Vasantha Kandasamy, K. Ilanthenral
Neutrosophic Graphs: A New Dimension To Graph Theory, Florentin Smarandache, Wb. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time have made a through study of neutrosophic graphs. This study reveals that these neutrosophic graphs give a new dimension to graph theory. The important feature of this book is it contains over 200 neutrosophic graphs to provide better understanding of this concepts. Further these graphs happen to behave in a unique way inmost cases, for even the edge colouring problem is different from the classical one. Several directions and dimensions in graph theory are obtained from this study. Finally certainly these new notions of neutrosophic graphs in general and in particular the …
Characterizing Conflict In Wikipedia, Nathaniel Miller
Characterizing Conflict In Wikipedia, Nathaniel Miller
Mathematics, Statistics, and Computer Science Honors Projects
Wikipedia serves as the Internet's most widely viewed reference. In order to ensure its success, editors who create and maintain articles must resolve conflicts over appropriate article content. Previous research has measured Wikipedia conflict at two levels: single articles and categories of pages. I observe conflicts within small groups of articles, identifying their frequency, size, and intensity. Additionally, I identify individual conflicts spanning multiple articles and effects of conflict upon users' editing habits. I analyze cross-article conflict in three stages. First, I cluster a group of 1.4 million Wikipedia articles. Next, I find individual user conflicts within each article cluster …
Results In Lattices, Ortholattices, And Graphs, Jianning Su
Results In Lattices, Ortholattices, And Graphs, Jianning Su
Doctoral Dissertations
This dissertation contains two parts: lattice theory and graph theory. In the lattice theory part, we have two main subjects. First, the class of all distributive lattices is one of the most familiar classes of lattices. We introduce "π-versions" of five familiar equivalent conditions for distributivity by applying the various conditions to 3-element antichains only. We prove that they are inequivalent concepts, and characterize them via exclusion systems. A lattice L satisfies D0π, if a ✶ (b ✶ c) ≤ (a ✶ b) ✶ c for all 3-element antichains { a, b, c}. We consider …