In recent years extensive research has been done on visibility graphs. In this thesis, we study some of the visibility graph algorithms, and implement these algorithms in the graph editor - GraphPerfect - which is a part of a project headed by Dr. Jay S. Bagga of the Department of computer science at Ball State University. One of the goals of this project is to design and build a software tool to learn and work with graphs and graph algorithms.In this thesis, some properties of visibility graphs are studied in detail and implementation of some graph algorithms is given. / Department of Computer Science

The hypercube is one of the most versatile and efficient networks yet discovered for parallel computation. It is well suited for both special-purpose and general-purpose tasks, and it can efficiently simulate many other networks of the same size. The size of subgraphs can be used to estimate the efficient communications of hypercube computer systems.The thesis investigates induced subgraphs of a hypercube, discusses sizes of subgraphs, and provides a formula to give bounds on the size of any subgraph of the hypercube.The concept of spanning graphs and line graphs is useful for studying properties of graphs. An MS WINDOWS based graphical system is developed which allows the creation and display of graphs and their spanning graphs, line graphs and super line graphs. / Department of Computer Science

Very large graphs are difficult for a person to browse and edit on a computer screen. This thesis introduces a visual formalism, structured graphs, which supports the scalable browsing and editing of very large graphs. This approach is relevant to a given application when it incorporates a large graph which is composed of named nodes and links, and abstraction hierarchies which can be defined on these nodes and links. A typical browsing operation is the selection of an arbitrary group of nodes and the display of the network of nodes and links for these nodes. Typical editing operations is: adding a new link between two nodes, adding a new node in the hierarchy, and moving sub-graphs to a new position in the node hierarchy. These operations are scalable when the number of user steps involved remains constant regardless of how large the graph is. This thesis shows that with structured graphs, these operations typically take one user step. We demonstrate the utility of structured graph formalism in an application setting. Computer aided software engineering tools, and in particular, structured analysis tools, are the chosen application area for this thesis, as they are graph based, and existing tools, though adequate for medium sized systems, lack scalability. In this thesis examples of an improved design for a structured analysis tool, based on structured graphs, is given. These improvements include scalable browsing and editing operations to support an individual software analyst, and component composition operations to support the construction of large models by a group of software analysts. Finally, we include proofs of key properties and descriptions of two text based implementations.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 88-92). Also available via the Internet.

Thesis (Ph. D.)--University of Pennsylvania, 1930.

Thesis (Ph. D.) in Psychology--University of Maine, 2001. / Includes vita. Includes bibliographical references (leaves 162-174).

Thesis (Ph. D.)--Washington State University, August 2009. / Title from PDF title page (viewed on Aug. 19, 2009). "School of Electrical Engineering and Computer Science." Includes bibliographical references (p. 114-117).

The behaviour of very low frequency (V.L.F.) radio waves propagating in an ionlzed medium, such as the ionosphere and exosphere, may exhibit markedly different characteristics from those of frequencies such as are used for communication in the short-wave bands. The anisotropy introduced into the medium by the presence of the earth's magnetic field has a significant effect, while at frequencies below about 5KHz the presence of heavy positive ions may further affect propagation. In particular it is found that, under suitable conditions, V.L.F. signals may propagate along paths closely following the lines of force of the earth's magnetic field. The study of such signals has a practical interest in that, from consideration of their propagation times and dispersion properties, they can provide an inexpensive method of determining electron densities at well beyond the range of satellite investigation. For this reason, if for no other, theoretical investigation of the paths traced in a model exosphere may indicate how closely the model exosphere approximates the true one. A powerful method of tracing out these paths is by the use of "ray-tracing", provided the properties of the medium vary slowly in space, a condition not always fulfilled in practice. It has been the subject of this thesis to carry out ray-tracing studies, in particular noting the effects of the positive ions in the exosphere; effects which have not received much notice before as they were thought to be unimportant. Intro., p. 1-2.

This study is concerned with how children interpret the slope of a line graph. Today with the vast accumulations of data which are available from computers, people are being faced with an ever increasing amount of pictorial representation of this data. Therefore it is of the utmost importance that children understand pictorial representation. Yet in spite of the popularity of graphs as tools of communication, studies show that many adults experience difficulty in reading information presented in a graphical form. The slope of the graph was chosen for this investigation because it is in this aspect of graphing (as shown by the results of the 1981 B.C. Assessment) that children in British Columbia seem to have the greatest difficulty when they reach Grade 8. The study dealt with positive, negative, zero and infinite slopes, combinations of these slopes, curvilinear graphs and qualitative graphs, that is, graphs that have no numerical data shown on the axes. The researcher chose to use a structured individual interview as a means of collecting data about how the students interpreted the slope of a line graph. Graphs used in the interviews dealt with temperature, height, weight and distance. Twenty-two students were chosen for this study. The students were found to have problems mainly with graphs dealing with distance related to time. This problem may be due to the fact that many students read only one axis and when interpreting distance seem to include direction as an added dimension of the graph. Infinite slope graphs were misinterpreted by every student, which may be due to the fact that they ignore the time axis. In general students used two methods of interpreting graphs. In some cases they observed the direction of the graph from left to right, that is, whether the slope went up or down from left to right. In other cases they examined the end points on the graph and drew their conclusions from them. The choice of method varied with the contextual material shown on the graph, which may be due to the children's concept of the parameter in the physical world and whether they see the parameter as being able to increase and decrease over time. From the study the investigator feels that more discussion of graphing by teachers and students is needed if the misconceptions are to be cleared up. Discussion of the parameters of both axes by teachers might help clear up the misconceptions students have about distance travelled over a period of time when this is expressed as a graph. There would be less chance of a graph being read as a map if the relationships between the two axes were demonstrated to students. Teachers also need to be aware of both methods used by students in interpreting graphs. / Education, Faculty of / Graduate

Ph.D. / In this thesis, the ranks of many types of regular and strongly regular graphs are determined. Also determined are ranks of regular graphs under unary operations: the line graph, the complement, the subdivision graph, the connected cycle, the complete subdivision graph, and the total graph. The binary operations considered are the Cartesian product and the complete product. The ranks of the Cartesian product of regular graphs have been investigated previously in [BBD1]; here, we summarise and extend those results to include more regular graphs. We also examine a special nonregular graph, the path. Ranks of paths and products of graphs involving paths are presented as well