在張宜武教授的博士論文中研究到視線表示法和視線數。我們以類似的方法定義有向圖的表示法和有向圖的視線數。
首先，我們定義有向圖的視線數為b(Ｄ) ，Ｄ為有方向性的圖，在論文中可得b(Ｄ)≦┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐。另一個重要的結論為考慮一個平面有向圖Ｄ，對圖形Ｄ上所有的點v，離開點v的邊（進入的邊）是緊鄰在一起時，則可得有向圖的視線數在這圖形上是１（即 b(Ｄ)=1）。
另外對特殊的圖形也有其不同的視線數，即對有向完全偶圖Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐ ，而對競賽圖Ｄn ，可得b(Ｄn)≦┌n/3┐+1。 / In [2], Chang stuidied the bar visibility representations and defined bar visibility number.We defined analogously the bar visibility representation and the bar visibility number of a directed graph Ｄ.
First we show that the bar visibility number, denoted by b(Ｄ),is at most ┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐ if D is an oriented graph.And we show that b(Ｄ)=1 for the oriented planar graphs in which all outgoing (incoming) edges of any vertex v of Ｄ appear consecutively around v.For any complete bipartite digraph Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐.For any tournament Ｄn,b(Ｄn)≦┌n/3┐+1.
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002001695 |
| Creators | 曾煥絢, Tseng, Huan-Hsuan |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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