Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2014-01-01

Journal: GRAPHS AND COMBINATORICS

Included Journals: SCIE

Volume: 30

Issue: 1

Page Number: 247-251

ISSN: 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.