| Summary: | 碩士 === 國立交通大學 === 應用數學研究所 === 82 === The $type$ of a vertex $v$ in a $p$-page book-embedding is the
$p\times 2$ matrix of nonnegative integers \[ \begin{array}{c}
\tau (v)\\ \end{array} = \left[ \begin{array}{cc} l_{v,1}&
r_{v,1}\\ \vdots & \vdots \\ l_{v,p}&r_{v,p}\\ \end{array} \
right], \] where $l_{v,i}$(respectively, $r_{v,i}$) is the
number of edges incident to $v$ that connect on page $i$ to
vertices lying to the left (respectively, to the right) of $v$.
The $ typenumber $ of a graph $G,$ $T(G)$, is the minimum
number of different types among all the book-embeddings of G.
In this thesis, we shall consider the general properties of
$typenumber$ and the $typenumber$ of some specific graphs.
Mainly, we find an upper bound for lattice graph, $L_{m,n}$,
and give exact solutions when $m\le 3$. In case that $m=2$ and
$n\geq 3$, our result disprove the conjecture by J. Buss et.al.
which says for $n\ge 4$, $T(L_{2,n})$ is not less than 5.
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