Opuscula Math. 37, no. 3 (2017), 447-456

Opuscula Mathematica

On the inverse signed total domination number in graphs

D. A. Mojdeh
B. Samadi

Abstract. In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on \(K_{r+1}\)-free graphs for \(r\geq 2\). Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.

Keywords: inverse signed total dominating function, inverse signed total domination number, \(k\)-tuple total domination number.

Mathematics Subject Classification: 05C69.

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  • D. A. Mojdeh
  • University of Mazandaran, Department of Mathematics, Babolsar, Iran
  • B. Samadi
  • University of Mazandaran, Department of Mathematics, Babolsar, Iran
  • Communicated by Dalibor Fronček.
  • Received: 2016-07-12.
  • Revised: 2016-12-08.
  • Accepted: 2016-12-10.
  • Published online: 2017-01-30.
Opuscula Mathematica - cover

Cite this article as:
D. A. Mojdeh, B. Samadi, On the inverse signed total domination number in graphs, Opuscula Math. 37, no. 3 (2017), 447-456, http://dx.doi.org/10.7494/OpMath.2017.37.3.447

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