中文摘要：

由把尽可能少的测量设备放在系统监视一个电力系统的问题仔细在图理论与盖住并且统治的著名顶点有关被给问题。在这份报纸，力量支配与直径一张 outerplanar 图数，这被显示出二或有直径的一张 2-connected outerplanar 图三正是一个。力量支配上的上面的界限与直径为一张一般的平面图数二或三是被决定一 Dorfling 证明的结果的立即的后果，等。另外，有直径的 outerplanar 图的一个无限的家庭四个有的任意地大的力量支配数字被给。

英文摘要：

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In this paper, it was shown that the power domination number of an outerplanar graph with the diameter two or a 2-connected outerplanar graph with the diameter three is precisely one. Upper bounds on the power domination number for a general planar graph with the diameter two or three were determined as an immediate consequences of results proven by Dorfling, et al. Also, an infinite family of outerplanar graphs with the diameter four having arbitrarily large power domination numbers were given.