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LSU Doctoral Dissertations

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Distributed Load Testing By Modeling And Simulating User Behavior, Chester Ira Parrott Dec 2020

Distributed Load Testing By Modeling And Simulating User Behavior, Chester Ira Parrott

LSU Doctoral Dissertations

Modern human-machine systems such as microservices rely upon agile engineering practices which require changes to be tested and released more frequently than classically engineered systems. A critical step in the testing of such systems is the generation of realistic workloads or load testing. Generated workload emulates the expected behaviors of users and machines within a system under test in order to find potentially unknown failure states. Typical testing tools rely on static testing artifacts to generate realistic workload conditions. Such artifacts can be cumbersome and costly to maintain; however, even model-based alternatives can prevent adaptation to changes in a system …


Experiential Statistics: A Case Study In Favor Of Using Project-Based Learning To Advance Preliminary Statistics Content Knowledge In The Algebra I And Geometry Classroom, Trey Michael Earle Dec 2020

Experiential Statistics: A Case Study In Favor Of Using Project-Based Learning To Advance Preliminary Statistics Content Knowledge In The Algebra I And Geometry Classroom, Trey Michael Earle

LSU Doctoral Dissertations

Preparing secondary students for college entrance requirements and the expectations of the job market, a market which is actively seeking the employees who are most qualified to take on jobs that require data analysis skills, is becoming increasingly important. Federal, state, and local education administrators and personnel must rewrite many of the general education curricula to incorporate data organization, collection, manipulation, application, and analysis in order to better prepare students for the expectations of college entrance and an ever-changing employment market. From a purely pedagogical standpoint, while traditional educational structure has been commonplace for decades in the United States, projects …


Synthesis Of Structurally Diverse Molecular Scaffolds Enabled By Protected Oxyallyl Cations, Joshua Andrew Malone Dec 2020

Synthesis Of Structurally Diverse Molecular Scaffolds Enabled By Protected Oxyallyl Cations, Joshua Andrew Malone

LSU Doctoral Dissertations

This dissertation focuses on the synthesis of diverse molecular scaffolds through the use of protected oxyallyl cation intermediates. Chapter One provides background on the generation and applications of oxyallyl and silyloxyallyl cations, while focusing on the direct nucleophilic capture of theses intermediates to generate functionalized ketones and silylenolates. Chapter Two depicts our approach to generate six-membered silyloxyallyl cations through the use of mild Brønsted acid activation. Regioselective nucleophilic capture of these intermediates successfully produced diverse a,a’-substituted silylenol ethers enabled by polar solvent and residual water.

Chapter three details strategies to generate 1,4-dicarbonyl compounds, focusing on the capture of cationic intermediates …


Machine Learning Based Applications For Data Visualization, Modeling, Control, And Optimization For Chemical And Biological Systems, Yan Ma Dec 2020

Machine Learning Based Applications For Data Visualization, Modeling, Control, And Optimization For Chemical And Biological Systems, Yan Ma

LSU Doctoral Dissertations

This dissertation report covers Yan Ma’s Ph.D. research with applicational studies of machine learning in manufacturing and biological systems. The research work mainly focuses on reaction modeling, optimization, and control using a deep learning-based approaches, and the work mainly concentrates on deep reinforcement learning (DRL). Yan Ma’s research also involves with data mining with bioinformatics. Large-scale data obtained in RNA-seq is analyzed using non-linear dimensionality reduction with Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP), followed by clustering analysis using k-Means and Hierarchical Density-Based Spatial Clustering with Noise (HDBSCAN). This report focuses …


Fluid-Driven Fracture Initiation From Oil And Gas Wells Considering Lifetime Stresses, Andreas Michael Nov 2020

Fluid-Driven Fracture Initiation From Oil And Gas Wells Considering Lifetime Stresses, Andreas Michael

LSU Doctoral Dissertations

Fluid-driven fracture initiation from oil and gas wells is examined in detail. The dissertation covers three subtopics: drilling, completion (stimulations), and post-blowout capping-induced fracture initiation.

Drilling-induced tensile fractures (DITFs) are located in an azimuth orthogonal to wellbore breakouts and are observed from image logs obtained during drilling operations. Fully analytical criteria for the orientation of DITFs initiating from wells in porous, permeable media are derived considering fluid infiltration from a pressurized wellbore. DITF orientation (longitudinal or transverse-to-the-wellbore) is used to constrain the magnitude of the local maximum horizontal principal stress. The range of the possible stress states is indicated on …


Measurements And Mitigation Of Scattered Light Noise In Ligo, Corey Daniel Austin Nov 2020

Measurements And Mitigation Of Scattered Light Noise In Ligo, Corey Daniel Austin

LSU Doctoral Dissertations

The Advanced LIGO (aLIGO) detectors use 1064 nm lasers to measure the tiny fluctuations in spacetime that occur when gravitational waves pass through the earth. LIGO makes use of advanced coating methods and materials to limit the amount of light that scatters from the main beam, but some amount of light does scatter. This stray light can interact with surfaces inside the interferometer that are not seismically isolated and then recombine with the main beam, introducing excess noise into the gravitational wave channel. This thesis reviews the methods for modeling scattered light with ray tracing software and analytical models, for …


Deep-Ultraviolet Laser Ablation For Biomolecular Analysis, Oluwaremilekun Omowunmi Lawal Nov 2020

Deep-Ultraviolet Laser Ablation For Biomolecular Analysis, Oluwaremilekun Omowunmi Lawal

LSU Doctoral Dissertations

New sampling and ionization techniques were developed using a deep-ultraviolet (DUV) laser at 193 nm wavelength for analysis of large biomolecules. A micrometer spatial resolution DUV laser ablation and capture system was constructed to sample tissue biomolecules. The spot size measurements of the focused beam showed that subcellular spots with ca. 2 μm diameter can be readily achieved with this wavelength. To demonstrate the extraction of tissue biomolecules with the DUV laser, regions of tissue sections were ablated and captured for offline proteomic and genomic analysis. The proteomic studies revealed that the tissue proteins were ejected without fragmentation and that …


Sustainable Management Of Groundwater In Louisiana, Dependra Bhatta Nov 2020

Sustainable Management Of Groundwater In Louisiana, Dependra Bhatta

LSU Doctoral Dissertations

The common property nature of the Mississippi River Alluvial Aquifer (MRAA) results in the formation of a cone of depression in the southern portion of the aquifer encompassing Concordia parish, Louisiana. Excessive groundwater withdrawal and the resulting cone of depression formation have caused some wells to go dry and others to be affected by saltwater intrusion. The depleting groundwater stock can be managed optimally using different groundwater management policies. The findings of this dissertation are relevant to both policymakers and researchers to understand the effects of policies to keep the aquifer sustainable.

My dissertation is written in a three-essay format. …


Structure And Dynamics Of Phospholipid Vesicles And The Dependence On Nanoscale Interactions With Molecules Of Varying Complexity, Lakshapathy Widanelage Judith Upeka De Mel Nov 2020

Structure And Dynamics Of Phospholipid Vesicles And The Dependence On Nanoscale Interactions With Molecules Of Varying Complexity, Lakshapathy Widanelage Judith Upeka De Mel

LSU Doctoral Dissertations

In this dissertation, molecular interactions and changes imposed by nano-scale structures on phospholipid vesicles were investigated. 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) large unilamellar vesicles (LUVs) were used as the model system. Understanding changes of the bilayer structure, interfacial properties, lipid dynamics, and self-assembly, allows bridging relationships between biological cell membrane structure and dynamics to cellular functionalities. For example, membrane curvature changes are linked to membrane protein functions, although the exact mechanisms of control are not yet understood. Moreover, the knowledge gained from vesicle models allows exploring novel strategies for drug delivery applications. To achieve this, DOPC LUVs were synthesized and characterized by a …


Computational Investigations Of Battery Electrolytes, Ke Li Nov 2020

Computational Investigations Of Battery Electrolytes, Ke Li

LSU Doctoral Dissertations

In this dissertation, the structure and dynamics of battery electrolytes were investigated using atomistic molecular dynamics (MD) simulations. Battery electrolytes play a key role in transporting ions between the cathode and anode. The chemical stability and ionic conductivity of electrolytes influence battery performance. In order to design better electrolytes, one needs an understanding of the relationship between electrolyte structure, dynamics, and bulk properties. To bridge the gap between the macroscopic phenomenon and the hidden molecular physics, in the first project we focused on probing an ether-based electrolyte, chosen for its relevance in sodium-based batteries. Through studying the impact of concentration …


Adsorption And Reconfiguration Of Amphiphiles At Silica-Water Interfaces: Role Of Electrostatic Interactions, Van Der Waals Forces And Hydrogen Bonds, Yao Wu Nov 2020

Adsorption And Reconfiguration Of Amphiphiles At Silica-Water Interfaces: Role Of Electrostatic Interactions, Van Der Waals Forces And Hydrogen Bonds, Yao Wu

LSU Doctoral Dissertations

The ability to explore and predict metastable structures of hybrid self-assemblies is of central importance for the next generation of advanced materials with novel properties. As compared to their thermodynamically stable forms, the kinetically stabilized materials show improved functionality potentially over their stable counterparts. The self-assembly processes usually originate from weak intermolecular interactions, involving a dynamic competition between attractive and repulsive interactions. These weak forces, including van der Waals (vdW), electrostatic interaction and the hydrogen bonding (H-bonding), can be tuned by external stimuli, e.g., confinement, temperature and ionization, and consequently driving hybrid materials into different configurations. It is challenging to …


Methods For 1,2-Cis-Selective O-Glycosylation And Synthesis Of An A. Baumannii Lipooligosaccharide Core Disaccharide, Ashley Fulton Nov 2020

Methods For 1,2-Cis-Selective O-Glycosylation And Synthesis Of An A. Baumannii Lipooligosaccharide Core Disaccharide, Ashley Fulton

LSU Doctoral Dissertations

This dissertation focuses on the formation of organic thin films on gold surfaces and synthesis of oligosaccharides. Chapter one, is a brief introduction on the utility of thin films, as well as ways to characterize thin films, as well as, a report on the attempt to form organic thin films on Au(111) surfaces using photoredox catalysis.

Glycoconjugates on cell surfaces serve as important mediators of intercellular recognition, adhesion, and viral infection. Due to the significant role that glycoconjugates play on the surface of cells, oligosaccharide synthesis is of great interest. Chapter two, is an extensive review of oligosaccharide synthesis, its …


Synthesis And Investigation Of Amphiphilic Polypeptoids For Environmental And Biological Applications, Tianyi Yu Nov 2020

Synthesis And Investigation Of Amphiphilic Polypeptoids For Environmental And Biological Applications, Tianyi Yu

LSU Doctoral Dissertations

Polypeptoids are an emerging class of peptidomimetic polymers featuring N-substituted polyglycine backbones. Polypeptoids are cyto-compatible and backbone degradable, making them appealing to many biological applications. When the highly polar polyamide backbone is coupled with non-polar aliphatic side chains, polypeptoids can be considered as facial amphiphiles. Without extensive hydrogen bonding along the backbone, the conformation of polypeptoid is largely controlled by the N-substituent structures. The hydrophobicity-lipophilicity balance of polypeptoids can be readily tuned with the N-substituent structures as well as the molar ratio between the hydrophilic and hydrophobic segments in their copolymers. In view of these combined attributes, …


A Study Of 26al(P, Γ)27si With The Silicon Array For Branching Ratio Experiments (Sabre), Erin Courtney Good Nov 2020

A Study Of 26al(P, Γ)27si With The Silicon Array For Branching Ratio Experiments (Sabre), Erin Courtney Good

LSU Doctoral Dissertations

The observation of the radioisotope 26Al is an indicator of ongoing nucleosynthesis in the Galaxy due to its short lifetime (t1/2 = 7.2 × 105 yr) on Galactic timescales. It is thought to be synthesized in several different environments in our Galaxy, one of which is in classical novae. Classical novae are stellar explosions that occur on the surface of a white dwarf in a binary system with a main sequence star. The isotopic production resulting from the nucleosynthesis that drives these explosions can be modeled with the input of nuclear reaction rates. In recent years, many …


A Phase-Field Approach To Diffusion-Driven Fracture, Friedrich Wilhelm Alexander Dunkel Oct 2020

A Phase-Field Approach To Diffusion-Driven Fracture, Friedrich Wilhelm Alexander Dunkel

LSU Doctoral Dissertations

In recent years applied mathematicians have used modern analysis to develop variational phase-field models of fracture based on Griffith's theory. These variational phase-field models of fracture have gained popularity due to their ability to predict the crack path and handle crack nucleation and branching.

In this work, we are interested in coupled problems where a diffusion process drives the crack propagation. We extend the variational phase-field model of fracture to account for diffusion-driving fracture and study the convergence of minimizers using gamma-convergence. We will introduce Newton's method for the constrained optimization problem and present an algorithm to solve the diffusion-driven …


Parallel And Asynchronous Distributed Optimization For Power Systems Operation, Ali Mohammadi Oct 2020

Parallel And Asynchronous Distributed Optimization For Power Systems Operation, Ali Mohammadi

LSU Doctoral Dissertations

Distributed optimization approaches are gaining more attention for solving power systems energy management functions, such as optimal power flow (OPF). Preserving information privacy of autonomous control entities and being more scalable than centralized approaches are two primary reasons for developing distributed algorithms. Moreover, distributed/ decentralized algorithms potentially increase power systems reliability against failures of components or communication links.

In this dissertation, we propose multiple distributed optimization algorithms and convergence performance enhancement techniques to solve the OPF problem. We present a multi-level optimization algorithm, based on analytical target cascading, to formulate and solve a collaborative transmission and distribution OPF problem. This …


Adaptive Data Migration In Load-Imbalanced Hpc Applications, Parsa Amini Oct 2020

Adaptive Data Migration In Load-Imbalanced Hpc Applications, Parsa Amini

LSU Doctoral Dissertations

Distributed parallel applications need to maximize and maintain computer resource utilization and be portable across different machines. Balanced execution of some applications requires more effort than others because their data distribution changes over time. Data re-distribution at runtime requires elaborate schemes that are expensive and may benefit particular applications.

This dissertation discusses a solution for HPX applications to monitor application execution with APEX and use AGAS migration to adaptively redistribute data and load balance applications at runtime to improve application performance and scaling behavior. This dissertation provides evidence for the practicality of using the Active Global Address Space as is …


Using Spatial Analysis And Machine Learning Techniques To Develop A Comprehensive Highway-Rail Grade Crossing Consolidation Model, Samira Soleimani Oct 2020

Using Spatial Analysis And Machine Learning Techniques To Develop A Comprehensive Highway-Rail Grade Crossing Consolidation Model, Samira Soleimani

LSU Doctoral Dissertations

The safety of highway-railroad grade crossings (HRGC) is still an issue in the United States of America (USA). The grade crossing is where a railroad crosses a road at the same level without any over or underpass. To improve the safety of crossings, the crossings’ condition should be explored from several aspects such as engineering design (speed limit, warning signs, etc.), road condition (number of lanes, surface markings, etc.), rail design (the type of track, ballast, etc.), temporal variables (weather, visibility, time of day, lightning, etc.), social variables (population, race, etc.), and last but not least, spatial variables (the type …


Point-Of-Care Devices For Therapeutic, Medical And Environmental Applications, Alisha Prasad Sep 2020

Point-Of-Care Devices For Therapeutic, Medical And Environmental Applications, Alisha Prasad

LSU Doctoral Dissertations

Point-of-care testing (POCT) or Point-of-use (POU) devices or technologies are defined as testing aids that are capable for onsite use or testing. The key advantages of POCT are low sample volume, quick onsite diagnosis, high accuracy, and cost-effectiveness. POCT has the potential and the benefits to facilitate better health care management by rapid routine diagnosis and monitoring. To reach this goal, several researchers as well as the healthcare industry over a few years have conducted cutting edge research to bring science to technology by developing smart diagnostic devices capable of performing as per patient profiles and make personalized health care …


Numerical Modeling Of Wave- And Current-Supported Turbidity Currents Over Erodible Bed, Sahar Haddadian Aug 2020

Numerical Modeling Of Wave- And Current-Supported Turbidity Currents Over Erodible Bed, Sahar Haddadian

LSU Doctoral Dissertations

The physical processes that route sediments from nearshore to the continental margin provide vital information to the global assessment of the geochemically important matter and the life in the ocean. Therefore, understanding these processes at the fundamental level will help develop accurate models that can be integrated into operational ocean models. Wave- and current-supported turbidity currents (WCSTCs) are one of the mechanisms that deliver sediments to the continental margin. WCSTCs are slow-moving turbidity currents where near-bed turbulence driven by strong surface waves and/or currents, tide- and/or wind-driven, maintain the turbidity current in motion. This study investigates the along-shelf current-supported turbidity …


Modeling Anatomic Changes For Adaptive Radiotherapy In Locally Advanced Lung Cancer Patient Population, James Alexander Kavanaugh Aug 2020

Modeling Anatomic Changes For Adaptive Radiotherapy In Locally Advanced Lung Cancer Patient Population, James Alexander Kavanaugh

LSU Doctoral Dissertations

Anatomic changes occurring mid-treatment for patients undergoing radiation therapy for locally advanced lung cancer can degrade the quality of the intended treatment plan. These changes include tumor regression, geometric misalignment, and lung density changes (atelectasis and pleural effusion), and are visible on the daily 3D cone beam CT (CBCT). To maintain the intended treatment quality, adaptive radiotherapy (ART) can be employed to modify the treatment plan to account for these anatomic changes. However, the evaluation on when to adapt is currently completed manually by the treating clinicians, resulting in a subjective and inconsistent application. To address these limitations, a series …


Methodologies For Improvement Of Metal Fatigue Life, Ali Haghshenas Aug 2020

Methodologies For Improvement Of Metal Fatigue Life, Ali Haghshenas

LSU Doctoral Dissertations

A methodology is proposed to identify the onset of crack initiation that utilizes the material damping. The damping is measured using the impulse excitation technique (IET). The damping is also used to correlate fatigue life of additively manufactured (AM) specimens to their damping characteristics. Results reveal that the damping value is inversely proportional to the fatigue life of the specimens.

To detect the damage accumulation and crack initiation in metals due to cyclic loading, another methodology based on the measurement of the surface roughness parameters is introduced. Results presented reveal that the evolution of the surface roughness parameters can be …


Moderators Of Academic Performance And Symptom Severity In Adolescents With Attention-Deficit/Hyperactivity Disorder, Ryan Nicole Cummins Aug 2020

Moderators Of Academic Performance And Symptom Severity In Adolescents With Attention-Deficit/Hyperactivity Disorder, Ryan Nicole Cummins

LSU Doctoral Dissertations

Research has documented the relationship between attention-deficit/hyperactivity disorder (ADHD) symptom severity and poor academic outcomes. However, few studies have focused on identifying moderating variables of academic performance specific to adolescents, especially those with ADHD. The current study seeks to address these limitations, further exploring moderators of academic outcomes in a clinical sample of adolescents with ADHD. Specifically, the present study examined adolescent ratings of routines, parent-adolescent conflict, perceptions of parental involvement, and school engagement, on the relationship between ADHD symptom severity and academic performance (GPA). The sample consisted of a total of 140 caregiver-adolescent dyads ranging from ages 11- to …


Development Of Artificial Intelligence Approach To Nowcasting And Forecasting Vibrio Prevalence In Coastal Waters, Peyman Hosseinzadeh Namadi Aug 2020

Development Of Artificial Intelligence Approach To Nowcasting And Forecasting Vibrio Prevalence In Coastal Waters, Peyman Hosseinzadeh Namadi

LSU Doctoral Dissertations

Vibrio parahaemolyticus (V.p) is an epidemiologically significant pathogen that poses high risks to the human health and shellfish industry, calling for predictive models for management interventions. This study presents an Artificial Intelligence(AI)-based approach to predicting and reducing the risks. The AI-based approach involves the identification of environmental indicators and their optimum variation ranges favoring V.p prevalence, the development of nowcasting and forecasting models for predicting V.p prevalence, and the creation of remote sensing algorithms for mapping concentrations of V.p and its environmental indicators by synergistically combining the Deep Neural Network (DNN) modeling technique, Genetic Programming (GP) method, R …


Transition Metal Complexes Of Pyridyltriazole And Bipyridine Ligands, Sen Gao Aug 2020

Transition Metal Complexes Of Pyridyltriazole And Bipyridine Ligands, Sen Gao

LSU Doctoral Dissertations

Four Ni(II) complexes have been obtained with the pyridyltriazole ligand, bpt, or the bis(pyridyltriazole) ligand, m-xpt, in chapter 2. This work was carried out as a comparison with the previously established coordination chemistry of copper(II) with bpt and m-xpt. Initially, the reaction between Ni(II) and bpt only produced one mononuclear compound, [Ni(bpt)2(H2O)2](NO3)2 (1). In order to study the formation of Ni-bpt and Ni-m-xpt complexes in solution, mixtures of Ni(NO3)2 and ligand (m-xpt or bpt) were prepared in different ratios and …


Second Harmonic Generation Spectroscopy And Microscopy Of Liposomes, Nanoparticles, And Cells, Prakash Hamal Aug 2020

Second Harmonic Generation Spectroscopy And Microscopy Of Liposomes, Nanoparticles, And Cells, Prakash Hamal

LSU Doctoral Dissertations

Second harmonic generation (SHG) is used to investigate the factors that impact nanoparticle-based drug-delivery applications. In the first study, molecular adsorption and transport kinetics of a positively-charged dye, malachite green isothiocyanate (MGITC), is characterized at the surface of different colloidal liposomes in water using SHG spectroscopy. The molecular interactions of MGITC is compared to our previous investigations with malachite green (MG). In comparison to MG, MGITC demonstrates stronger adsorption and faster transport through lipid membranes. Correspondingly, the SHG experimental results are in excellent agreement with the molecular dynamics (MD) simulations results. A key finding illustrates the importance of functional groups, …


Pressure Monitoring For Subsurface Leakage Characterization, Mojtaba Mosaheb Jul 2020

Pressure Monitoring For Subsurface Leakage Characterization, Mojtaba Mosaheb

LSU Doctoral Dissertations

Undesirable leakage from underground sedimentary formations is a matter of considerable concern due to implications for water resources contamination and greenhouse gas emissions. Leakage in underground formations can remain undetected for a long period. Pressure monitoring is a dynamic method that can be used for leakage detection and characterization. The pressure signals are affected by the hydraulic characteristics of the reservoir media and leakage pathways. Consequently, the pressure data can be interpreted to obtain information about the hydraulic characteristics of the system. Pressure interpretation is useful for early leakage detection, because the pressure signals travel fast in reservoir media. In …


Habitat Fragmentation And Range Margin Effects On Dispersal And Interactions Between Competitors, Rachel Roxann Harman Jul 2020

Habitat Fragmentation And Range Margin Effects On Dispersal And Interactions Between Competitors, Rachel Roxann Harman

LSU Doctoral Dissertations

Dispersal is a fundamental process that affects local and regional dynamics, including population persistence, range expansion, and interspecific interactions, particularly as disturbance through habitat fragmentation and climate change. Here, my main objective was to ascertain how fragmentation affects dispersal and the interactions of competitors within the local patch and regional landscape. In my second chapter, I assessed dispersal through a literature review and population persistence model to examine the breadth and frequency of different density-emigration forms that occur in nature, including forms that are not prevalent in the literature. I conclude that these rare forms have important population dynamic consequences …


Solvation Structures And Dynamics Of Small Molecules: Experimental And Computational Studies Using Carbonyl Vibrational Modes As Probe, Xiaoliu Zhang Jul 2020

Solvation Structures And Dynamics Of Small Molecules: Experimental And Computational Studies Using Carbonyl Vibrational Modes As Probe, Xiaoliu Zhang

LSU Doctoral Dissertations

Solutions are ubiquitous in both the global environment and the human body, and play a significant role in scientific research and industrial production. The structures and dynamics of solutions have been studied for centuries. However, conventional experimental methods, whose intrinsic measuring time is on the order of nanoseconds to microseconds, could not detect the fast dynamics taking place in the solution on the timescale of femto- and pico-second. In this dissertation, the ultrafast two-dimensional infrared (2DIR) spectroscopy was applied to characterize the structure and dynamics in three different types of solutions on the sub-picosecond timescale. Linear Fourier transform infrared spectroscopy …


Some Results On Seymour’S Second-Neighborhood Conjecture And On Decompositions Of Graphs, Farid Bouya Jul 2020

Some Results On Seymour’S Second-Neighborhood Conjecture And On Decompositions Of Graphs, Farid Bouya

LSU Doctoral Dissertations

This dissertation consists of two parts. In the first part, I examine Seymour’s Second-Neighborhood Conjecture, which states that every orientation of every simple graph has at least one vertex v such that the number of vertices of out-distance 2 from v is at least as large as the number of vertices of out-distance 1 from it. I present alternative statements of this conjecture using the language of linear algebra, the last one being completely in terms of the inverse of some matrix. In the second part of this dissertation, comprising of Chapters 2 and 3, I examine two conjectures on …