"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling." / Doctor of Philosophy

The research presented in this thesis investigates the performance of some well-known heuristic algorithms on graph decomposition problems. First, a genetic algorithm is introduced and some modifications are trialled on finding Steiner triple systems (STS) of small orders. The results show that traditional genetic algorithms are not well suited to finding graph decompositions. Then a hill climbing optimisation technique is presented and investigated in the context of cycle decompositions. Such searches have previously proved to be effective at finding STSs. However, the general hill climbing approach is not immediately applicable to decompositions into cycles of length larger than 3. A modification of the hill climbing algorithm for cycles, called slippery hill climbing, is introduced and tested on decompositions of graphs into cycles of small lengths larger than 3. Slippery hill climbing successfully decomposed complete and dense non-complete graphs of considerable sizes into cycles of small lengths. In addition, we applied the slippery hill climbing approach to completing partial latin squares. It is reasonably expected that the algorithms developed in this study will also be applicable to other related problems in combinatorics and graph theory.

"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling." / Doctor of Philosophy

Research. Thesis (M.Sc.)--University of Melbourne, Dept. of Computer Science and Software Engineering, 2006. / Typescript. Includes bibliographical references (leaves 163-170).

Thesis (Ph. D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Thomas, Robin; Committee Co-Chair: Cook, William J.; Committee Member: Dvorak, Zdenek; Committee Member: Parker, Robert G.; Committee Member: Yu, Xingxing.

Thesis (M.C.S.) - Carleton University, 2005. / Includes bibliographical references (p. 127-130). Also available in electronic format on the Internet.

Thesis (Ph.D.)--Computing, Georgia Institute of Technology, 2009. / Committee Chair: Bader, David; Committee Member: Berry, Jonathan; Committee Member: Fujimoto, Richard; Committee Member: Saini, Subhash; Committee Member: Vuduc, Richard

Thesis (M.S.)--University of North Texas, Dec., 2009. / Title from title page display. Includes bibliographical references.

Thesis (M.S.)--University of North Carolina at Wilmington, 2005. / Includes bibliographical references (leaves: 60-61)

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Computer Science, 2009. / Includes bibliographical references.