A Characterization of Cubic Graphs with Paired-Domination Number Three-Fifths Their Order

作者：Goddard Wayne^*; Henning Michael A

来源：Graphs and Combinatorics, 2009, 25(5): 675-692.

DOI：10.1007/s00373-010-0884-2

• Bounds
• Cubic graphs
• Paired-domination
• Petersen graph

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.

• 出版日期2009-11