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 在這篇論文中，我們藉由討論線星數和星數之間的關係得到線星數的邊界值。我們藉由星數得到線星數的上界為：$s^*(G) \leq 3s(G)$。當我們限制某些induced subgraphs，我們得到線星數的上界。當G沒有induced $K_4-{e}$， 我們得到$s^*(G) \leq s(G)+1$。而且，triangle-free graph 的線星數上界也是 $s(G)+1$。 當圖形G的$\triangle (G)=3$，我們得到星數等於線星數。圖形G的$\triangle (G)=４$，我們也可得到 $s(G)+1$。
 In this thesis, we study relationships between linear star number and star number and obtain bounds on the linear star number. We obtain an upper bound on linear star number in term of star number: $s^*(G) \leq 3s(G)$. When we forbid certain induced subgraphs, we obtain an upper bound on linear star number. If G is a graph without induced $K_4-{e}$, we prove that $s^*(G) \leq s(G)+1$. And, the linear star number of the triangle-free graph is also bounded by s(G)+1. The linear star number and star number are equal when G is a graph with $\triangle (G)=3.$ When G is a graph with $\triangle (G)=4$. , we also obtain $s(G)+1$.
 1 Introduction 2 A General Upper Bound of Linear star Number 3 Bounds of Linear Star Number in Restricted classes
 @BOOK{texbook,author = {Douglas B. West},year = 1996,title = {Introduction to Graph Theory},publisher = {PRENTICE HALL}}@ARTICLE{Gav,author={F. Gavril},title={The intersection graphs of subtrees in trees are exactly the chordal graphs},journal={J. Combinatorics Theory B},volume={16},year={1974},pages={45-56},}@ARTICLE{Bun,author={P.A. Buneman},title={A characterization of rigid circuit graphs},journal={Discrete Math},volume={9},year={1974},pages={205-212},}@ARTICLE{Wal,author={J.R. Walter},title={Representations of chordal graphs as subtrees of a tree},journal={J. Graph Theory},volume={2},year={1978},pages={265-267},}@ARTICLE{Wes,author={D.B. West},title={Parameters in partial orders and graphs:Packing, covering, and representation},journal={Graphs and Order},volume={2},year={1985},pages={267-350},}% --------------------------------------------------------------------------@PHDTHESIS{Chang,author={Yi-Wu Chang},title={Graph Representations Using Star, Tree, Intervals And Boxes},school={M.S., University of Illinois},year={1994},}% ------------------------------------------------------------------------
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