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Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux
Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux
Electronic Theses and Dissertations
In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or …
Double Domination Of Complementary Prisms., Lamont D. Vaughan
Double Domination Of Complementary Prisms., Lamont D. Vaughan
Electronic Theses and Dissertations
The complementary prism of a graph G is obtained from a copy of G and its complement G̅ by adding a perfect matching between the corresponding vertices of G and G̅. For any graph G, a set D ⊆ V (G) is a double dominating set (DDS) if that set dominates every vertex of G twice. The double domination number, denoted γ×2(G), is the cardinality of a minimum double dominating set of G. We have proven results on graphs of small order, specific families and lower bounds on γ×2 …
Finding Edge And Vertex Induced Cycles Within Circulants., Trina Marcella Wooten
Finding Edge And Vertex Induced Cycles Within Circulants., Trina Marcella Wooten
Electronic Theses and Dissertations
Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As …
Roles Of Gap Junctions In Neuronal Networks, Joon Ha
Roles Of Gap Junctions In Neuronal Networks, Joon Ha
Dissertations
This dissertation studies the roles of gap junctions in the dynamics of neuronal networks in three distinct problems. First, we study the circumstances under which a network of excitable cells coupled by gap junctions exhibits sustained activity. We investigate how network connectivity and refractory length affect the sustainment of activity in an abstract network. Second, we build a mathematical model for gap junctionally coupled cables to understand the voltage response along the cables as a function of cable diameter. For the coupled cables, as cable diameter increases, the electrotonic distance decreases, which cause the voltage to attenuate less, but the …
Machine Learning And Graph Theory Approaches For Classification And Prediction Of Protein Structure, Gulsah Altun
Machine Learning And Graph Theory Approaches For Classification And Prediction Of Protein Structure, Gulsah Altun
Computer Science Dissertations
Recently, many methods have been proposed for the classification and prediction problems in bioinformatics. One of these problems is the protein structure prediction. Machine learning approaches and new algorithms have been proposed to solve this problem. Among the machine learning approaches, Support Vector Machines (SVM) have attracted a lot of attention due to their high prediction accuracy. Since protein data consists of sequence and structural information, another most widely used approach for modeling this structured data is to use graphs. In computer science, graph theory has been widely studied; however it has only been recently applied to bioinformatics. In this …
Biological Networks: Modeling And Structural Analysis, Emad Y. Ramadan
Biological Networks: Modeling And Structural Analysis, Emad Y. Ramadan
Computer Science Theses & Dissertations
Biological networks are receiving increased attention due to their importance in understanding life at the cellular level. There exist many different kinds of biological networks, and different models have been proposed for them. In this dissertation we focus on suitable network models for representing experimental data on protein interaction networks and protein complex networks (protein complexes are groups of proteins that associate to accomplish some function in the cell), and to design algorithms for exploring such networks. Our goal is to enable biologists to identify the general principles that govern the organization of protein-protein interaction networks and protein complex networks. …