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Articles 1 - 30 of 57
Full-Text Articles in Physical Sciences and Mathematics
Dominating Functions In Graphs, Maria Talanda-Fisher
Dominating Functions In Graphs, Maria Talanda-Fisher
Dissertations
Domination in graphs has become one of the most popular areas of graph the- ory, no doubt due to its many fascinating problems and applications to modern society, as well as the sheer mathematical beauty of the subject. While this area evidently began with the work by the French mathematician Claude Berge in 1958 and the Norwegian-American mathematician Oystein Ore in 1962, domination did not become an active area of research until 1977 with the appearance of the survey paper by Ernest Cockayne and Stephen Hedetniemi. Since then a large number of variations of domination have surfaced and provided numerous …
Color-Connected Graphs And Information-Transfer Paths, Stephen Devereaux
Color-Connected Graphs And Information-Transfer Paths, Stephen Devereaux
Dissertations
The Department of Homeland Security in the United States was created in 2003 in response to weaknesses discovered in the transfer of classied information after the September 11, 2001 terrorist attacks. While information related to national security needs to be protected, there must be procedures in place that permit access between appropriate parties. This two-fold issue can be addressed by assigning information-transfer paths between agencies which may have other agencies as intermediaries while requiring a large enough number of passwords and rewalls that is prohibitive to intruders, yet small enough to manage. Situations such as this can be represented by …
Structures Of Derived Graphs, Khawlah Hamad Alhulwah
Structures Of Derived Graphs, Khawlah Hamad Alhulwah
Dissertations
One of the most familiar derived graphs are line graphs. The line graph L(G) of a graph G is the graph whose vertices are the edges of G where two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. One of the best- known results on the structure of line graphs deals with forbidden subgraphs by Beineke. A characterization of graphs whose line graph is Hamiltonian is due to Harary and Nash-Williams. Iterated line graphs of almost all connected graphs were shown to be Hamiltonian by Chartrand. The girth of a graph G …
Highly Hamiltonian Graphs And Digraphs, Zhenming Bi
Highly Hamiltonian Graphs And Digraphs, Zhenming Bi
Dissertations
A cycle that contains every vertex of a graph or digraph is a Hamiltonian cycle. A graph or digraph containing such a cycle is itself called Hamiltonian. This concept is named for the famous Irish physicist and mathematician Sir William Rowan Hamilton. These graphs and digraphs have been the subject of study for over six decades. In this dissertation, we study graphs and digraphs with even stronger Hamiltonian properties, namely highly Hamiltonian graphs and digraphs.
Edge Colorings Of Graphs And Their Applications, Daniel Johnston
Edge Colorings Of Graphs And Their Applications, Daniel Johnston
Dissertations
Edge colorings have appeared in a variety of contexts in graph theory. In this work, we study problems occurring in three separate settings of edge colorings.
For more than a quarter century, edge colorings have been studied that induce vertex colorings in some manner. One research topic we investigate concerns edge colorings belonging to this class of problems. By a twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of …
Secondary Mathematics Teachers’ Attitudes And Beliefs Toward Statistics: Developing An Initial Profile, Christina M. Zumbrun
Secondary Mathematics Teachers’ Attitudes And Beliefs Toward Statistics: Developing An Initial Profile, Christina M. Zumbrun
Dissertations
Over the last several decades, mathematics education researchers have given increased attention to students’ and teachers’ attitudes and beliefs toward mathematics and statistics, but no work has been done that examines practicing secondary mathematics teachers’ (SMTs’) attitudes and beliefs towards statistics in light of the GAISE framework and the Common Core State Standards for Mathematics (CCSSM). This study begins to address this gap in the research by creating the Teacher Attitude and Beliefs toward Statistics Survey (TABSS), a synthesis of items taken from the Survey of Attitudes Toward Statistics (Schau, 2003), the Statistics Course Attitude Scale and newly developed items …
Modular Monochromatic Colorings, Spectra And Frames In Graphs, Chira Lumduanhom
Modular Monochromatic Colorings, Spectra And Frames In Graphs, Chira Lumduanhom
Dissertations
Abstract attached as separate document.
On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews
On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews
Dissertations
Abstract attached as separate file.
Modular And Graceful Edge Colorings Of Graphs, Ryan Jones
Modular And Graceful Edge Colorings Of Graphs, Ryan Jones
Dissertations
Abstract attached as separate file.
Hamiltonicity And Connectivity In Distance-Colored Graphs, Kyle C. Kolasinski
Hamiltonicity And Connectivity In Distance-Colored Graphs, Kyle C. Kolasinski
Dissertations
Abstract attached as separate file.
Understanding Similarity: Bridging Geometric And Numeric Contexts For Proportional Reasoning, Dana Christine Cox
Understanding Similarity: Bridging Geometric And Numeric Contexts For Proportional Reasoning, Dana Christine Cox
Dissertations
The concept of similarity is uniquely situated at the crossroads of geometric and numerical proportional reasoning. Although studies have documented the existence and nature of student difficulties with this topic, there exists a gap between documented visual insights of younger children and the quantitative inadequacies of older ones. Using a revised version of the Similarity Perception Test followed by 21 clinical interviews, this study investigated the visual and analytical strategies that are used by middle-school students to differentiate and construct similar figures.
New strategies for construction and differentiation were identified, and three overarching conclusions were drawn from the work. First, …
What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz
What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz
Dissertations
Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how …
The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui
The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui
Dissertations
In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dvs ), where dvs ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The …
Measures Of Travers Ability In Graphs, Futaba Okamoto
Measures Of Travers Ability In Graphs, Futaba Okamoto
Dissertations
For a connected graph G of order n ≥ 3 and a cyclic ordering sc : v 1, v2,..., vn, v n+1 = v1 of vertices of G, the number d(sc) is defined by d(sc) = i=1n d(vi, vi +1), where d(vi, vi +1) is the distance between vi and vi+1 in G for 1 ≤ i ≤ n. The Hamiltonian number h(G) and upper Hamiltonian number h +(G) of G are defined as h(G) = min{d(sc)} and h+(G) = max{d(sc)}, respectively, where the minimum and maximum are taken over all cyclic orderings s c of vertices of G. For …
Stratification And Domination In Graphs And Digraphs, Ralucca M. Gera
Stratification And Domination In Graphs And Digraphs, Ralucca M. Gera
Dissertations
In this thesis we combine the idea of stratification with the one of domination in graphs and digraphs, respectively.
A graph is 2-stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v . An F -coloring of a graph G is a red-blue coloring of the vertices of G in which every blue vertexu belongs to a copy of F rooted at u . The F -domination number γ …
Structure Preserving Algorithms For Computing The Symplectic Singular Value Decom Position, Archara Chaiyakarn
Structure Preserving Algorithms For Computing The Symplectic Singular Value Decom Position, Archara Chaiyakarn
Dissertations
In this thesis we develop two types of structure preserving Jacobi algorithms for com puting the symplectic singular value decomposition of real symplectic matrices and complex symplectic matrices. Unlike general purpose algorithms, these algorithms produce symplectic structure in all factors of the singular value decomposition.
Our first algorithm uses the relation between the singular value decomposition and the polar decomposition to reduce the problem of finding the symplectic singular value decomposition to th a t of calculating the structured spectral decomposition of a doubly structured m atrix. A Jacobi-like m ethod is developed to compute this doubly structured spectral decomposition. …
Global Optimality Conditions In Mathematical Programming And Optimal Control, Pariwat Pacheenburawaa
Global Optimality Conditions In Mathematical Programming And Optimal Control, Pariwat Pacheenburawaa
Dissertations
We derive new first-order necessary and sufficient optimality conditions characterizing global minimizers in mathematical programming and optimal controlproblems. These conditions are based on level sets of an objective functional and they do not assume special structure of a problem (convexity, linearity, etc.). For a mathematical programming problem of minimization of a smooth functional on some compact convex set with equality nonlinear constraints, we derive first-order optimality conditions in the form of a generalized Lagrange multiplier rule. This rule should hold for any point from the level set of the objective functional corresponding to a global minimizer. We demonstrate that these …
An Investigation Of Secondary Teachers’ Knowledge Of Rate Of Change In The Context Of Teaching A Standards-Based Curriculum, Jihwa Noh
Dissertations
This study investigated teachers' mathematical content knowledge and pedagogical content knowledge with respect to rate of change in the context of teaching a Standards-based high school mathematics curriculum that emphasizes rate of change as a central theme, the Core-Plus Mathematics Project (CPMP) materials. A framework was designed to provide a comprehensive guide for analyzing different aspects of rate of change knowledge incorporating existing frameworks relative to rate of change, NCTM recommendations described in Curriculum and Evaluation Standards for School Mathematics andPrinciples and Standards for School Mathematics (NCTM, 2000), and research related to pedagogical understanding of rate of change.
Data …
New Graphical Approach On The Analysis Of Experimental Data, Suha Sari
New Graphical Approach On The Analysis Of Experimental Data, Suha Sari
Dissertations
This study presents a new graphical method to identify significant effects in factorial experiments. The proposed methods are obtained for the different cases in which the design can be of full factorial or fractional factorial and the factor levels can be pure or mixed.
We focus on the different decomposition methods, for example orthogonal components system and orthogonal contrast method, to make use of the chisquare plot which requires that the sums of squares are of the same degrees of freedom. Examples and simulations illustrating the different cases of the procedure are presented.
Resolvability In Graphs, Varaporn Saenpholphat
Resolvability In Graphs, Varaporn Saenpholphat
Dissertations
The distance d (u, v ) between two vertices u and v in a connected graph G is the length of a shortest u - v path in G . For an ordered set W = { w1 , w2 , [Special characters omitted.] &cdots; , wk } of vertices in G and a vertex v of G , the code of v with respect to W is the k -vector cW (v ) = (d ( v, w1 ),d (v, w 2 ), [Special characters omitted.] &cdots; , d …
Cost Domination In Graphs, David John Erwin
Cost Domination In Graphs, David John Erwin
Dissertations
Let G be a connected graph having order at least 2. A function f : V (G) —> {0 , 1 , . . . , diam G} for which f ( v ) < e(v) for every vertex v of G is a cost function on G. A vertex v with f ( v ) > 0 is an f-dominating vertex, and the set Vj~ = {v 6 V(G) : f(v) > 0} of f-dominating vertices is the f-dominating set. An /-dominating vertex v is said to f-dominate every vertex u with d(n, v) < f(u ), while …
A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones
A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones
Dissertations
A central question in the area of topological graph theory is to find the genus of a given graph. In particular, the genus parameter has been studied for Cayley graphs. A Cayley graph is a representation of a group and a fixed generating set for that group. A group is said to be planar if there is a generating set which produces a planar Cayley graph. We say that a group is toroidal if there is a generating set that produces a toroidal Cayley graph and if there are no generating sets which produce a planar Cayley graph. Characterizations for …
Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann
Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann
Dissertations
No abstract provided.
Domination In Digraphs, Lisa Hansen
A Robust Estimate For An Autoregressive Time Series, Jeffrey Terpstra
A Robust Estimate For An Autoregressive Time Series, Jeffrey Terpstra
Dissertations
A weighted rank-based estimate for estimating the parameter of an auto-regressive time series is considered. When the weights are constant, the estimate is equivalent to using Jaeckel’s estimate and Wilcoxon scores. The estimate can be shown to be asymptotically normal at rate y/n. In a linear regression setting this estimate has the desired properties of a continuous totally bounded influence function and a positive breakdown point. It is shown via examples and Monte Carlo that these properties are preserved in an autoregressive time series setting.
Integrity Of Digraphs, Robert Charles Vandell
Integrity Of Digraphs, Robert Charles Vandell
Dissertations
The vertex-integrity of a digraph D, denoted I(D), is defined to be the minimum over aIII subsets X of the vertex set of D for the quantity IXI + m(D - X), w here IXI is the number of vertices in X and m(D - X) is the maximum order of a strong component in the digraph D - X. In a like manner, the arc-integrity of the digraph D, denoted I’(D), is defined to be the minimum over all subsets Y of the arc set of D for the quantity IYI + m(D - Y), where IYI is the …
Step Domination In Graphs, Kelly Lynne Schultz
Step Domination In Graphs, Kelly Lynne Schultz
Dissertations
One of the major areas in Graph Theory is domination in graphs. It is this area with which this dissertation deals, with the primary emphasis on step domination in graphs.
In Chapter 1 we present some preliminary definitions and examples. In addition, a background of the area of domination is presented. We then introduce the concepts that lead to step domination.
In Chapter II we formally define the concept of step domination and give several examples. We determine the minimum number of vertices needed in a step domination set for many classes of graphs. We then explore step domination for …
Asymptotic Diagonalizations Of A Linear Ordinary Differential System, Feipeng Xie
Asymptotic Diagonalizations Of A Linear Ordinary Differential System, Feipeng Xie
Dissertations
No abstract provided.
Probability Polynomials For Cubic Graphs In The Framework Of Random Topological Graph Theory, Esther Joy Tesar
Probability Polynomials For Cubic Graphs In The Framework Of Random Topological Graph Theory, Esther Joy Tesar
Dissertations
Topological graph theorists study the imbeddings of graphs on surfaces (spheres with handles). Some interesting questions in the field are on w hat surfaces can a graph be 2 -cell imbedded and how m any such imbeddings are there on each surface. The study of these and related questions is called Enumerative Topological Graph Theory. Random Topological Graph Theory uses probability models to study the 2-cell imbeddings. It generalizes the results from Enumerative Topological Graph Theory (which is the uniform case, p= 1/2) to an arbitrary probability p.
We study the model where the sample space consists of all labeled, …
Semi-Strongly Regular Graphs And Generalized Cages, Cong Fan
Semi-Strongly Regular Graphs And Generalized Cages, Cong Fan
Dissertations
Two well-known classes of graphs, strongly regular graphs and cages, have been studied extensively by many researchers for a long period of time. In this dissertation, we mainly deal with semi-strongly regular graphs, a class of graphs including all strongly regular graphs, and (r, g, t)-cages, a generalization of the usual cage concept.
Chapter I introduces the two new concepts: semi-strongly regular graphs and generalized (r, g, t)-cages, gives necessary conditions for the existence of semi-strongly regular graphs and some interesting properties regarding common neighbors of pairs of vertices, and shows connections between these two new concepts and the old …