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Indexed by:期刊论文

Date of Publication:2014-01-01

Journal:GRAPHS AND COMBINATORICS

Included Journals:SCIE

Volume:30

Issue:1

Page Number:247-251

ISSN No.:0911-0119

Key Words:Double domination; Double domination number; Double domination subdivision number

Abstract: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.