On edge domination numbers of graphs

Let γ s ′ ( G ) and γ ss ′ ( G ) be the signed edge domination number and signed star domination number of G , respectively. We prove that 2 n - 4 ⩾ γ ss ′ ( G ) ⩾ γ s ′ ( G ) ⩾ n - m holds for all graphs G without isolated vertices, where n = | V ( G ) | ⩾ 4 and m = | E ( G ) | , and pose some prob...

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Bibliographic Details
Published inDiscrete mathematics Vol. 294; no. 3; pp. 311 - 316
Main Author Xu, Baogen
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 06.05.2005
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Signed edge domination function
Signed edge domination number
Signed star domination function
Signed star domination number
Signed edge domination number
Signed edge domination function
Signed star domination number
Signed star domination function
Edge(graph)
Domination function
Domination number
Graph theory
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Summary:Let γ s ′ ( G ) and γ ss ′ ( G ) be the signed edge domination number and signed star domination number of G , respectively. We prove that 2 n - 4 ⩾ γ ss ′ ( G ) ⩾ γ s ′ ( G ) ⩾ n - m holds for all graphs G without isolated vertices, where n = | V ( G ) | ⩾ 4 and m = | E ( G ) | , and pose some problems and conjectures.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2004.11.008