Opuscula Math. 37, no. 3 (2017), 447-456
http://dx.doi.org/10.7494/OpMath.2017.37.3.447

Opuscula Mathematica

# On the inverse signed total domination number in graphs

D. A. Mojdeh

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
• University of Mazandaran, Department of Mathematics, Babolsar, Iran
• Communicated by Dalibor Fronček.
• Revised: 2016-12-08.
• Accepted: 2016-12-10.
• Published online: 2017-01-30.