增廣體之泛連性質研究

Abstract

這篇論文裡，我們討論到增廣體的一般性質和泛連性質的進一步研究。增廣立方體是從超立方體衍生而出的另一種拓樸圖形並且有良好的幾何特性；一個連結圖如果擁有從最短路徑到漢米頓路徑之間所有長度的路徑，則稱此圖為泛連圖。在本文中，我們將會證明增廣體是泛連圖，並提出其它的泛連圖及性質。

In this paper，we discussed the general properties of augmented cubes and pan-connectivity. Augmented cubes are derivatives of cubes with good geometric nature. A graph G is pan-connected if there exists a path of length l joining any two vertices x and y with d(x,y) □ l □ | V(G)-1 |. In the content, we will prove that augmented cubes are pan-connected, and show some other pan-connected graphs.