| 具有小直径平面图的电力控制数 |
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| 引用本文： | 赵敏,康丽英.具有小直径平面图的电力控制数[J].上海大学学报(英文版),2007,11(3):218-222. |
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| 作者姓名： | 赵敏 康丽英 |
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| 作者单位： | Department of Mathematics College of Sciences，Shanghai University，Shanghai 200444，P. R. China，Department of Mathematics，College of Sciences，Shanghai University，Shanghai 200444，P. R. China |
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| 基金项目： | 国家自然科学基金;上海市青年科学基金 |
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| 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.
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| 关 键 词： | 图论 直径 平面图 曲面图 电力系统控制 |
| 文章编号： | 10.1007/s11741-007-0305-3 |
| 收稿时间： | 26 May 2005 |
| 修稿时间： | 2005-05-262005-06-27 |
Power domination in planar graphs with small diameter |
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| ZHAO Min,KANG Li-ying.Power domination in planar graphs with small diameter[J].Journal of Shanghai University(English Edition),2007,11(3):218-222. |
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| Authors: | ZHAO Min KANG Li-ying |
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| Institution: | Department of Mathematics,College of Sciences,Shanghai University,Shanghai 200444,P.R.China |
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| Abstract: | 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. |
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| Keywords: | graph power domination planar graph outerplanar graph |
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