在一圖形中之一k-中繼點控制集為一節點之子集合，而此子集合外之點相隔此控制集其中一點至多k個中繼點。若一k-中繼點控制集中之任兩點間皆存在經過控制集內之路徑，則稱其具有連結性(connected)。在無線隨意網路中之節點可藉由在頻道內傳送訊信息，或透過網路之路由(routing)與其鄰近節點進行溝通。經由階層式的路由協定來建立並維護具有連結性之k-中繼點控制集，可節省傳輸功率及網路溝通成本。本文發現一屬於具有連結性之k-中繼點控制集之特性，並證明：若圖中所有點皆符合此特性，則k-中繼點控制集具有連結性。且藉由此特性，建立並維護一具有連結性之k-中繼點控制集僅需2個中繼點之資訊。模擬結果顯示，隨著k遞增，所建立具有連結性之k-中繼點控制集也穩定地縮小。

In a graph G = (V,E), a k-hop dominating set Dk is a subset of such that all nodes in V are either in or at most k-hop to a node Dk. A k-hop dominating set Dk is connected if there is a path, in which each node is in Dk, between any two nodes in Dk. In a mobile ad hoc network, a node communicates with its neighbors by sending messages across channels, and the others by routing messages via the network. The hierarchical routing protocol that constructs and maintains a connected k-hop dominating set attempts to reduce transmission power and communication overhead. In this paper, the node property of a connected k-hop dominating set is found, and it is proved that a k-hop dominating set is connected if all nodes in V belong to the node property. By its aid, a connected k-hop dominating set is constructed and maintained using only 2-hop neighbor information. Our simulation shows that the connected dominating set shrinks consistently as the hop count of k grows.

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