# Twin Minus Total Domination Numbers In Directed Graphs

• Volume: 37, Issue: 4, page 989-1004
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Nasrin Dehgardi, and Maryam Atapour. "Twin Minus Total Domination Numbers In Directed Graphs." Discussiones Mathematicae Graph Theory 37.4 (2017): 989-1004. <http://eudml.org/doc/288581>.

@article{NasrinDehgardi2017,
abstract = {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.},
author = {Nasrin Dehgardi, Maryam Atapour},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {twin minus total dominating function; twin minus total domination number; directed graph.},
language = {eng},
number = {4},
pages = {989-1004},
title = {Twin Minus Total Domination Numbers In Directed Graphs},
url = {http://eudml.org/doc/288581},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Nasrin Dehgardi
AU - Maryam Atapour
TI - Twin Minus Total Domination Numbers In Directed Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 4
SP - 989
EP - 1004
AB - 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.
LA - eng
KW - twin minus total dominating function; twin minus total domination number; directed graph.
UR - http://eudml.org/doc/288581
ER -

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