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Bearing-Only Cooperative-Localization And Path-Planning Of Ground And Aerial Robots, Rajnikant Sharma
Bearing-Only Cooperative-Localization And Path-Planning Of Ground And Aerial Robots, Rajnikant Sharma
Theses and Dissertations
In this dissertation, we focus on two fundamental problems related to the navigation of ground robots and small Unmanned Aerial Vehicle (UAVs): cooperative localization and path planning. The theme running through in all of the work is the use of bearing only sensors, with a focus on monocular video cameras mounted on ground robots and UAVs. To begin with, we derive the conditions for the complete observability of the bearing-only cooperative localization problem. The key element of this analysis is the Relative Position Measurement Graph (RPMG). The nodes of an RPMG represent vehicle states and the edges represent bearing measurements …
Bounds For The Independence Number Of A Graph, William Willis
Bounds For The Independence Number Of A Graph, William Willis
Theses and Dissertations
The independence number of a graph is the maximum number of vertices from the vertex set of the graph such that no two vertices are adjacent. We systematically examine a collection of upper bounds for the independence number to determine graphs for which each upper bound is better than any other upper bound considered. A similar investigation follows for lower bounds. In several instances a graph cannot be found. We also include graphs for which no bound equals $\alpha$ and bounds which do not apply to general graphs.
Transcriptomic Data Analysis Using Graph-Based Out-Of-Core Methods, Gary L Rogers
Transcriptomic Data Analysis Using Graph-Based Out-Of-Core Methods, Gary L Rogers
Doctoral Dissertations
Biological data derived from high-throughput microarrays can be transformed into finite, simple, undirected graphs and analyzed using tools first introduced by the Langston Lab at the University of Tennessee. Transforming raw data can be broken down into three main tasks: data normalization, generation of similarity metrics, and threshold selection. The choice of methods used in each of these steps effect the final outcome of the graph, with respect to size, density, and structure. A number of different algorithms are examined and analyzed to illustrate the magnitude of the effects.
Graph-based tools are then used to extract putative gene networks. These …
A Characterization Of Ramsey Graphs For R(3,4), Nicholas M. Richardson
A Characterization Of Ramsey Graphs For R(3,4), Nicholas M. Richardson
Doctoral Dissertations
The Ramsey number R(ω, α) is the minimum number n such that every graph G with |V(G)| ≥ n has an induced subgraph that is isomorphic to a complete graph on ω vertices, Kω, or has an independent set of size α, Nα. Graphs having fewer than n vertices that have no induced subgraph isomorphic to K ω or Nα form a class of Ramsey graphs, denoted ℜ(ω, α). This dissertation establishes common structure among several classes of Ramsey graphs and establishes the complete list of ℜ(3, 4).
The process used to …
A Characterization Of Ramsey Graphs For R(3,4), Nicholas M. Richardson
A Characterization Of Ramsey Graphs For R(3,4), Nicholas M. Richardson
Doctoral Dissertations
The Ramsey number R(ω, α) is the minimum number n such that every graph G with |V(G)| ≥ n has an induced subgraph that is isomorphic to a complete graph on ω vertices, Kω, or has an independent set of size α, Nα. Graphs having fewer than n vertices that have no induced subgraph isomorphic to K ω or Nα form a class of Ramsey graphs, denoted ℜ(ω, α). This dissertation establishes common structure among several classes of Ramsey graphs and establishes the complete list of ℜ(3, 4).
The process used to …
Parity Domination In Product Graphs, Christopher Whisenant
Parity Domination In Product Graphs, Christopher Whisenant
Theses and Dissertations
An odd open dominating set of a graph is a subset of the graph’s vertices with the property that the open neighborhood of each vertex in the graph contains an odd number of vertices in the subset. An odd closed r-dominating set is a subset of the graph’s vertices with the property that the closed r-ball centered at each vertex in the graph contains an odd number of vertices in the subset. We first prove that the n-fold direct product of simple graphs has an odd open dominating set if and only if each factor has an odd open dominating …
Flanking Numbers And Its Application To Arankings Of Cyclic Graphs, M. Daniel Short
Flanking Numbers And Its Application To Arankings Of Cyclic Graphs, M. Daniel Short
Theses
Given a graph G with a ranking function, f: V(G) --> {1,2,...,k}, the ranking is minimal if only if G does not contain a drop vertex. The arank number of a graph, [psi]r(G), is the maximum k such that G has a minimal k-ranking. A new technique is established to better understand how to analyze arankings of various cyclic graphs, Cn. Then the technique, flanking number, is used to describe all arank properties of all cyclic graphs fully by proving the following proposition: [psi]r(C_n) = [floor]{log₂(n+1)[floor] + [floor]log₂(n+2/3)[floor] + 1 for all n > 6.
Universal Hypergraphs., Michael Deren
Universal Hypergraphs., Michael Deren
Electronic Theses and Dissertations
In this thesis, we study universal hypergraphs. What are these? Let us start with defining a universal graph as a graph on n vertices that contains each of the many possible graphs of a smaller size k < n as an induced subgraph. A hypergraph is a discrete structure on n vertices in which edges can be of any size, unlike graphs, where the edge size is always two. If all edges are of size three, then the hypergraph is said to be 3-uniform. If a 3-uniform hypergraph can have edges colored one of a colors, then it is called a …
A Predictive Model Which Uses Descriptors Of Rna Secondary Structures Derived From Graph Theory., Alissa Ann Rockney
A Predictive Model Which Uses Descriptors Of Rna Secondary Structures Derived From Graph Theory., Alissa Ann Rockney
Electronic Theses and Dissertations
The secondary structures of ribonucleic acid (RNA) have been successfully modeled with graph-theoretic structures. Often, simple graphs are used to represent secondary RNA structures; however, in this research, a multigraph representation of RNA is used, in which vertices represent stems and edges represent the internal motifs. Any type of RNA secondary structure may be represented by a graph in this manner. We define novel graphical invariants to quantify the multigraphs and obtain characteristic descriptors of the secondary structures. These descriptors are used to train an artificial neural network (ANN) to recognize the characteristics of secondary RNA structure. Using the ANN, …
The Roller-Coaster Conjecture, Leslie A. Cheteyan
The Roller-Coaster Conjecture, Leslie A. Cheteyan
Theses, Dissertations and Culminating Projects
No abstract provided.
Zero-Sum Magic Graphs And Their Null Sets, Samuel M. Hansen
Zero-Sum Magic Graphs And Their Null Sets, Samuel M. Hansen
UNLV Theses, Dissertations, Professional Papers, and Capstones
For any element h of the Natural numbers, a graph G=(V,E), with vertex set V and edge set E, is said to be h-magic if there exists a labeling of the edge set E, using the integer group mod h such that the induced vertex labeling, the sum of all edges incident to a vertex, is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h for which G admits a zero-sum h-magic labeling. A graph G is said to be uniformly …
Embeddings Of Product Graphs Where One Factor Is A Hypercube, Bethany Turner
Embeddings Of Product Graphs Where One Factor Is A Hypercube, Bethany Turner
Theses and Dissertations
Voltage graph theory can be used to describe embeddings of product graphs if one factor is a Cayley graph. We use voltage graphs to explore embeddings of various products where one factor is a hypercube, describing some minimal and symmetrical embeddings. We then define a graph product, the weak symmetric difference, and illustrate a voltage graph construction useful for obtaining an embedding of the weak symmetric difference of an arbitrary graph with a hypercube.
Probabilistic Problems In Graph Theory, Karen Rosemarie Johannson
Probabilistic Problems In Graph Theory, Karen Rosemarie Johannson
Electronic Theses and Dissertations
In this thesis, I examine two different problems in graph theory using probabilistic techniques. The first is a question on graph colourings. A proper total k-colouring of a graph G = (V, E) is a map φ : V υ E → {1, 2,…, k} such that φ|V is a proper vertex colouring, φ|E is a proper edge colouring, and if v V and vw E then φ(v) ≠ φ(vw). Such a colouring is called adjacent vertex distinguishing if for every pair of adjacent vertices, u and v, the set {φ(u)} υ {φ(uw) : uw E}, the `colour set of …
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 …
Hückel Energy Of A Graph: Its Evolution From Quantum Chemistry To Mathematics, Steven Zimmerman
Hückel Energy Of A Graph: Its Evolution From Quantum Chemistry To Mathematics, Steven Zimmerman
Electronic Theses and Dissertations
The energy of a graph began with German physicist, Erich H¨uckel’s 1931 paper, Quantenttheoretische Beitr¨age zum Benzolproblem. His work developed a method for computing the binding energy of the π-electrons for a certain class of organic molecules. The vertices of the graph represented the carbon atoms while the single edge between each pair of distinct vertices represented the hydrogen bonds between the carbon atoms. In turn, the chemical graphs were represented by an n × n matrix used in solving Schr¨odinger’s eigenvalue/eigenvector equation. The sum of the absolute values of these graph eigenvalues represented the total π-electron energy. The criteria …
Global Secure Sets Of Trees And Grid-Like Graphs, Yiu Yu Ho
Global Secure Sets Of Trees And Grid-Like Graphs, Yiu Yu Ho
Electronic Theses and Dissertations
Let G = (V, E) be a graph and let S ⊆ V be a subset of vertices. The set S is a defensive alliance if for all x ∈ S, |N[x] ∩ S| ≥ |N[x] − S|. The concept of defensive alliances was introduced in [KHH04], primarily for the modeling of nations in times of war, where allied nations are in mutual agreement to join forces if any one of them is attacked. For a vertex x in a defensive alliance, the number of neighbors of x inside the alliance, plus the vertex x, is at least the number …
Finding Dud Vertices In Defensive Alliances And Secure Sets Using Computational Tools, George Worley Ii
Finding Dud Vertices In Defensive Alliances And Secure Sets Using Computational Tools, George Worley Ii
Electronic Theses and Dissertations
Defensive alliances are a way of using graphs to model the defense of resources (people, buildings, countries, etc.) against attacks where the number of potential attackers against each resource is known. The initial study of defensive alliances focused on questions of minimal defensive alliances in a graph and the minimum possible size of a defensive alliance in a graph, but in order to apply defensive alliances in modeling real-world situations, additional considerations are important. In particular, since each vertex in a defensive alliance represents some real-world object that has a cost associated with remaining in the defensive alliance, it is …
New Statistical Methods To Derive Functional Connectivity From Multiple Spike Trains, Mohammad Shahed Masud
New Statistical Methods To Derive Functional Connectivity From Multiple Spike Trains, Mohammad Shahed Masud
Other Faculty of Science and Engineering Theses
Analysis of functional connectivity of simultaneously recorded multiple spike trains is one of the major issues in the neuroscience. The progress of the statistical methods to the analysis of functional connectivity of multiple spike trains is relatively slow. In this thesis two statistical techniques are presented to the analysis of functional connectivity of multiple spike trains. The first method is known as the modified correlation grid (MCG). This method is based on the calculation of cross-correlation function of all possible pair-wise spike trains. The second technique is known as the Cox method. This method is based on the modulated renewal …
Influence Maximization On Families Of Graphs, Andrei Mouravski
Influence Maximization On Families Of Graphs, Andrei Mouravski
Theses
We examine computing the maximum expected influence on paths and trees using the independent cascade model. We designed a polynomial time method for determining the expected influence from any initial state on the independent cascade model on acyclic influence graphs in O(|V(G)|² · max {|V(G)|,|V(E)|}) time. We designed a polynomial time program that would computes the maximum expected influence and optimal initially selected nodes on arbitrary paths in O(|V(T)|⁶/[epsilon]) on approximating the maximum expected influence on arbitrary trees with absolute error of at most ([epsilon] · 2|V(T)|).
Neighborhood Sum Parameters On Graphs, Frank Allen O'Neal
Neighborhood Sum Parameters On Graphs, Frank Allen O'Neal
Dissertations
No abstract provided.
Automatic Detection Of Inconsistencies In A Conceptual Graph Knowledge Base, Caralee Kassos
Automatic Detection Of Inconsistencies In A Conceptual Graph Knowledge Base, Caralee Kassos
Theses
No abstract provided.