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Original Article

On the trees with same signed edge and signed star domination numbers

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Pages 2388-2395 | Received 20 Jan 2015, Accepted 19 Sep 2017, Published online: 10 Nov 2017
 

ABSTRACT

Let γS(G) and γSS(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 order n3, if γS(T)=γSS(T)=k then k(3n+1)/5. Moreover, we prove that for any integer r1, there exists a tree Tr on n=5r+3 vertices such that γS(Tr)=γSS(Tr)=(3n+1)/5.

2010 AMS SUBJECT CLASSIFICATION:

Acknowledgments

The authors would like to thank the referees for valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Key Research and Development Program of China [grant number 2016YFB0800700] and National Natural Science Foundation of China [grant numbers 61672050, 61632002, 61502012 and 61572046].

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