A Characterization of Cubic Graphs with Paired-Domination Number Three-Fifths Their Order
A Characterization of Cubic Graphs with Paired-Domination Number Three-Fifths Their Order
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DOI：
10.1007/s00373-010-0884-2
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发表时间：
2009-11
影响因子：
0.7
通讯作者：
W. Goddard;Michael A. Henning
中科院分区：
文献类型：
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作者：
W. Goddard;Michael A. Henning
图的成对控制集是指其导出子图具有完美匹配的顶点的控制集，而成对控制数是指图中成对控制集的最小基数。最近，Chen et al. (Acta Math Sci Ser A Chin艾德27（1）：166-170，2007）证明了三次图的成对控制数至多为图中顶点数的五分之三。本文证明了Petersen图是唯一一个对控制数为其阶的五分之三的连通三次图。
A paired-dominating set of a graph is a dominating set of vertices whose induced subgraph has a perfect matching, while the paired-domination number is the minimum cardinality of a paired-dominating set in the graph. Recently, Chen et al. (Acta Math Sci Ser A Chin Ed 27(1):166–170, 2007) proved that a cubic graph has paired-domination number at most three-fifths the number of vertices in the graph. In this paper, we show that the Petersen graph is the only connected cubic graph with paired-domination number three-fifths its order.