Title page for etd-0116108-155641


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URN etd-0116108-155641
Author Ming-Hung Lin
Author's Email Address franklin641022@yahoo.com.tw
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Department Applied Mathematics
Year 2007
Semester 1
Degree Master
Type of Document
Language English
Title On the domination numbers of prisms of cycles
Date of Defense 2008-01-11
Page Count 24
Keyword
  • prism
  • cycle
  • domination number
  • Abstract Let $gamma(G)$ be the domination number of a graph $G$. For any
    permutation $pi$ 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 $vin
    V(G_{2})$ iff $v=pi(u)$. We prove that
    $$gamma(pi C_{n})geq cases{frac{ n}{ 2}, &if $n = 4k ,$ cr
    leftlceilfrac{n+1}{2}
    ight
    ceil, &if $n
    eq 4k$,} mbox{and }
    gamma(pi C_{n}) leq leftlceil frac{2n-1}{3}
    ight
    ceil
    mbox{for all }pi.$$ We also find a permutation $pi_{t}$ such that
    $gamma(pi_{t} C_{n})=k$, where $k$ between the lower bound and the
    upper bound of $gamma(pi C_{n})$ in above. Finally, we prove that
    if $pi_{b}C_{n}$ is a bipartite graph, then
    $$gamma(pi_{b}C_{n})geq cases{frac{n}{2}, &if $n = 4k ,$cr
    leftlceilfrac{n+1}{2}
    ight
    ceil, &if $n = 4k+2$,} mbox{and }
    gamma(pi_{b}C_{n})leq leftlfloor frac{5n+2}{8}
    ight
    floor.$$
    Advisory Committee
  • none - chair
  • none - co-chair
  • Li-Da Tong - advisor
  • Files
  • etd-0116108-155641.pdf
  • indicate access worldwide
    Date of Submission 2008-01-16

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