最近，Fujita [11] 提出了網路中的可移動式伺服器是否可以轉換佈署位置又同時不間斷的提供使用者服務的問題。我們稱使用者在某個網路節點可以使用伺服器所提供的服務，如果使用者所屬的網路節點的相鄰節點中（包括使用者本身所屬的節點在內）至少有一個節點佈署有伺服器。Fujita [11] 提出：對樹狀圖的網路結構而言，若要提供整個網路不間斷的服務，又要搬移伺服器的位置至另一種佈署位置，那大約需要整個網路節點的一半數量的伺服器。Fujita [11] 亦提出：對有漢彌爾頓圈的網路結構而言，若要提供整個網路不間斷的服務，又要搬移伺服器的位置至另一種佈署位置，那大約需要整個網路節點數量三分之一的伺服器。我們以圖 來表示網路結構。在這篇論文中，我們證明：若網路結構是強弦圖，則任兩個伺服器個數相同的控制集都足以保證「伺服器可以轉換佈署位置又同時提供整個網路不間斷的服務」。我們亦證明了：若網路結構是仙人掌圖，則任兩個伺服器個數相同的控制集只需加入一個額外的伺服器就足以保證「伺服器可以轉換佈署位置又同時提供整個網路不間斷的服務」。

Recently, Fujita [11] proposed a new framework to provide continuous services to users by a collection of mobile servers, and a user can receive the service if at least one adjacent node (including itself) has a mobile server. In [11], Fujita proved that for the class of trees of n vertices, [n/2] mobile servers are sometimes necessary
and always sucient to realize continuous services by the mobile servers, and for the class of Hamiltonian graphs of n vertices, [(n+1)/3]mobile servers are sometimes necessary and always sucient. In this thesis, we prove that for the class of connected strongly chordal graphs G, any two dominating sets of the same cardinality can be transferred to each other. We also prove that for the
class of cactus graphs, at most one extra mobile server has to be added so that any two dominating sets of the same cardinality can be transferred to each other.

Contents
1 Introduction P.1
2 Preliminaries P.4
3 Mutual transferability in connected strongly chordal graphs P.4
4 Mutual transferability in cactus graphs P.11
5 Concluding remarks P.18
References P.18

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