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论文类型：期刊论文

发表时间：2014-01-01

发表刊物：GRAPHS AND COMBINATORICS

收录刊物：SCIE

卷号：30

期号：1

页面范围：247-251

ISSN号：0911-0119

关键字：Double domination; Double domination number; Double domination subdivision number

摘要：A subset is a double dominating set of G if S dominates every vertex of G at least twice. The double domination number dd(G) is the minimum cardinality of a double dominating set of G. The double domination subdivision number sd (dd) (G) is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the double domination number. Atapour et al. (Discret Appl Math, 155:1700-1707, 2007) posed an open problem: Prove or disprove: let G be a connected graph with no isolated vertices, then 1 a parts per thousand currency sign sd (dd) (G) a parts per thousand currency sign 2. In this paper, we disprove the problem by constructing some connected graphs with no isolated vertices and double domination subdivision number three.