在網路的議題中，具有容錯性的廣播以及安全性的訊息分散皆擁有眾多應用。為了達到容錯及安全的需求，普遍的做法是以網路架構做為圖形結構，對其建構多棵擴展樹。我們將來源點當作樹根，複製k份的訊息，透過多棵擴展樹廣播至子結點，即可達到具有容錯性的廣播；另ㄧ方面，把訊息分割成k份，透過多棵擴展樹傳遞至子結點，便可達成安全訊息分散的目的。
一個圖形G的多棵擴展樹，如果有共同的樹根，而且它們兩兩之間任一點連接到樹根的路徑沒有使用共同的邊，則稱它們為一組邊互斥擴展樹。在最近的文獻中，Hsieh 和 Tu [Theoretical Computer Science 410 (2009) 926-932]提出一個能在n維局部扭轉超立方體上建構n棵邊互斥擴展樹的演算法，而局部扭轉超立方體是超立方體的變形。在本論文中，我們證明使用他們的演算法所建構出來的擴展樹其實為一組獨立擴展樹。換言之，任兩棵擁有共同樹根的擴展樹，任一點連接到樹根的路徑彼此為點互斥。

Fault-tolerant broadcasting and secure message distribution are important issues for numerous applications in networks. It is a common idea to design multiple spanning trees with a specific property in the underlying graph of a network to serve as a broadcasting scheme or a distribution protocol for receiving high levels of fault-tolerance and of security. The fault-tolerance can be achieved by sending k copies of the message and the security can be achieved by sending k parts of the message along the k spanning tree rooted at the source node. Recently, constructing multiple spanning trees of a given graph has received much attention.
A set of spanning trees in a graph G is said to be edge-disjoint if these trees are rooted at the same node without sharing any common edge. Hsieh and Tu [S.-Y. Hsieh and C.-J. Tu, Constructing edge-disjoint spanning trees in locally twisted cubes, Theoretical Computer Science 410 (2009) 926-932] recently presented an algorithm for constructing n edge-disjoint spanning trees in an n-dimensional locally twisted cube, which is a variant of the hypercube. In this thesis, we prove that indeed all spanning trees constructed by their algorithm are independent, i.e., any two spanning trees are rooted at the same node,say r, and for any other node v≠r, the two different paths from v to r, one path in each tree, are internally node-disjoint.

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