# Twin Minus Total Domination Numbers In Directed Graphs

Nasrin Dehgardi; Maryam Atapour

Discussiones Mathematicae Graph Theory (2017)

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

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topNasrin 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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