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On the inverse signed total domination number in graphs

Mojdeh D. A., Samadi B.

Opuscula Mathematica

2017

Vol. 37, no. 3

447--456

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 Kr+1-free graphs for r ≥ 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.

Bounds on the inverse signed total domination numbers in graphs

Atapour M., Norouzian S., Sheikholeslami S. M., Volkmann L.

Opuscula Mathematica

2016

Vol. 36, no. 2

145--152

Let G = (V, E) be a simple graph. A function ƒ : V→ {- 1,1} is called an inverse signed total dominating function if the sum of its function values over any open neighborhood is at most zero. The inverse signed total domination number of G, denoted by [formula], equals to the maximum weight of an inverse signed total dominating function of G. In this paper, we establish upper bounds on the inverse signed total domination number of graphs in terms of their order, size and maximum and minimum degrees.