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 in:Discrete mathematics 2005-05, Vol.294 (3), p.311-316
Main Author: Xu, Baogen
Format: Article
Language:English
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
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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