### Title page for etd-0116108-155641

URN etd-0116108-155641 Ming-Hung Lin franklin641022@yahoo.com.tw This thesis had been viewed 5224 times. Download 1145 times. Applied Mathematics 2007 1 Master English On the domination numbers of prisms of cycles 2008-01-11 24 prism cycle domination number Let \$gamma(G)\$ be the domination number of a graph \$G\$. For anypermutation \$pi\$ of the vertex set of a graph \$G\$, the prism of \$G\$with respect to \$pi\$ is the graph \$pi G\$ obtained from two copies\$G_{1}\$ and \$G_{2}\$ of \$G\$ by joining \$uin V(G_{1})\$ and \$vinV(G_{2})\$ iff \$v=pi(u)\$. We prove that\$\$gamma(pi C_{n})geq cases{frac{ n}{ 2}, &if \$n = 4k ,\$ crleftlceilfrac{n+1}{2}ightceil, &if \$n eq 4k\$,} mbox{and }gamma(pi C_{n}) leq leftlceil frac{2n-1}{3} ightceilmbox{for all }pi.\$\$ We also find a permutation \$pi_{t}\$ such that\$gamma(pi_{t} C_{n})=k\$, where \$k\$ between the lower bound and theupper bound of \$gamma(pi C_{n})\$ in above. Finally, we prove thatif \$pi_{b}C_{n}\$ is a bipartite graph, then\$\$gamma(pi_{b}C_{n})geq cases{frac{n}{2}, &if \$n = 4k ,\$crleftlceilfrac{n+1}{2}ightceil, &if \$n = 4k+2\$,} mbox{and }gamma(pi_{b}C_{n})leq leftlfloor frac{5n+2}{8}ightfloor.\$\$ none - chair none - co-chair Li-Da Tong - advisor indicate access worldwide 2008-01-16

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