The study of graph theory and its applications have increased substantially in the past 40 years. This is especially the case in the applications to the fields of computer science, electrical, and industrial engineering. Applications vary from designing computer software and hardware to telephone networks to airline network.In the thesis, properties are studied in detail to include definitions, theorems, examples and implementations of four graph algorithms in two important topics, namely connectivity and shortest paths. In the implementation part, algorithms will be available to solve problems on selected graphs. A graphic representation is also included to have a better picture of a problem and its solution. / Department of Computer Science

The Firefighter Process models the spread and defence of a fire using a simple graph. We consider the following discrete-time process: at t = 0 some vertex of the graph begins burning. At each subsequent step we may defend a vertex from burning and the fire spreads from all burning vertices to all undefended neighbours. We consider the related problems of maximising the number of saved vertices, protecting a specified set from burning and maximising the weight of the saved vertices. We close three open problems concerning these decision problems and their related optimisation problems using the notion of a strategy, the sequence of defended vertices. / Graduate

No description available.

No description available.

No description available.

Graduation date: 1992

Relational information visualisation concerns viewing relational data, where the underlying data model is a graph. Hierarchical visualisation is one of hot topics in graph visualisation in which the data is organised in a hierarchical structure. As the amount of information, that we want to visualise, becomes larger and the relations become more complex, classical visualisation techniques and hierarchical drawing methods tend to be inadequate.Traditional hierarchical visualisation algorithms are more concerned with the readability of the layouts. They usually do not consider the efficient utilisation of the geometrical plane for the drawings. Therefore, for most hierarchical layouts, a large portion of display space is wasted as background. The aim of this research is to investigate a space-efficient approach to handle the visualisation of large hierarchies in two-dimensional spaces. This thesis introduces a new graph visualisation approach called enclosure+ connection for visualizing large hierarchies. This approach maximises the space utilisation by taking advantages of the traditional enclosure partitioning approach, while it retains the display of a traditional node-link diagram to hopefully provide users a direct perception of relational structures. The main contribution of this thesis is layout and navigation algorithms for visualising large hierarchies. Two layout algorithms, the space-optimised tree and the EncCon tree, have been developed to achieve the space-efficient visualisation. Both algorithms use the enclosure concept to define layout of hierarchies, which ensure the efficient utilisation of display space. Two focus+context navigation and interaction methods have been proposed to cooperate with the visualization of large hierarchies. Several advanced computer graphics approaches, such as graphic distortion and transparency, are used for the development of these navigation methods. Two case studies have been implemented to evaluate the layout algorithms and the associated navigation methods. The first case study is an application of a shared collaborative workspace which aims to provide users with a better assistance for visual manipulation and navigation of knowledge-based information. The second case study is a visual browser for navigating large-scale online product catalogues. Although the case studies have provided some useful evaluation, formal usability studies would be required to justify fully the effectiveness of these layout and navigation methods. Although this task has not carried out in this research, the author has presented his usability study's plan as a future work.

Thesis (Ph.D.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (ℓ. 39)

Thesis (M.S.)--University of Nevada, Reno, 2006. / "December, 2006." Includes bibliographical references (leaves 49-50). Online version available on the World Wide Web.

Thesis (M.S.)--Georgia State University, 2007. / Title from file title page. Guantao Chen, committee chair; Michael Stewart, Yi Zhao, committee members. Electronic text ( 50 p.) : digital, PDF file. Description based on contents viewed Nov. 5, 2007. Includes bibliographical references (p. 49).