Let D = (V,A) be a finite simple directed graph (shortly, digraph). A function f : V → {−1, 0, 1} is called a twin minus total dominating function (TMTDF) if f(N−(v)) ≥ 1 and f(N+(v)) ≥ 1 for each vertex v ∈ V. The twin minus total domination number of D is y*mt(D) = min{w(f) | f is a TMTDF of D}. In this paper, we initiate the study of twin minus total domination numbers in digraphs and we present some lower bounds for y*mt(D) in terms of the order, size and maximum and minimum in-degrees and out-degrees. In addition, we determine the twin minus total domination numbers of some classes of digraphs.
@article{bwmeta1.element.doi-10_7151_dmgt_1983,
author = {Nasrin Dehgardi and Maryam Atapour},
title = {Twin Minus Total Domination Numbers In Directed Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {989-1004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1983}
}
Nasrin Dehgardi; Maryam Atapour. Twin Minus Total Domination Numbers In Directed Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 989-1004. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1983/