On the trees with same signed edge and signed star domination numbers. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Li, Zepeng; Xu, Jin
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 12(2018)
• Page Start: 2388
• Page End: 2395
• Publication Date: 2018-12-02
• Subjects: Tree -- signed edge domination function -- signed edge domination number -- signed star domination function -- signed star domination number; 05C05 -- 05C69; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1396453
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: Letγ S ′ ( G ) andγ S S ( G ) be the signed edge domination number and signed star domination number of a graph G, respectively. In this paper, we prove that for a tree T of ordern ≥ 3, ifγ S ′ ( T ) = γ S S ( T ) = k thenk ≥ ( 3 n + 1 ) / 5 . Moreover, we prove that for any integerr ≥ 1, there exists a treeT r on n =5 r +3 vertices such thatγ S ′ ( T r ) = γ S S ( T r ) = ( 3 n + 1 ) / 5 .