Geodesic
A characterization of graphs with disjoint total dominating sets
Ars mathematica contemporanea, Tome 16 (2019) no. 2, pp. 359-375 Cet article a éte moissonné depuis la source Ars Mathematica Contemporanea website

Voir la notice de l'article

A set S of vertices in a graph G is a total dominating set of G if every vertex is adjacent to a vertex in S. A fundamental problem in total domination theory in graphs is to determine which graphs have two disjoint total dominating sets. In this paper, we solve this problem by providing a constructive characterization of the graphs that have two disjoint total dominating sets. Our characterization gives an entirely new description of graphs with two disjoint total dominating sets and places them in another context, developing them from four base graphs and applies a sequence of operations from seventeen operations that are independent and necessary to produce all such graphs. We show that every graph with two disjoint total dominating sets can be constructed using this method.
DOI : 10.26493/1855-3974.1525.7f3
Keywords: Total domination number, disjoint total dominating sets 
@article{10_26493_1855_3974_1525_7f3,
     author = {Michael A. Henning and Iztok Peterin},
     title = {
		{A} characterization of graphs with disjoint total dominating sets
	},
     journal = {Ars mathematica contemporanea},
     pages = {359--375},
     year = {2019},
     volume = {16},
     number = {2},
     doi = {10.26493/1855-3974.1525.7f3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1525.7f3/}
}
TY  - JOUR
AU  - Michael A. Henning
AU  - Iztok Peterin
TI  - A characterization of graphs with disjoint total dominating sets
	
JO  - Ars mathematica contemporanea
PY  - 2019
SP  - 359
EP  - 375
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1525.7f3/
DO  - 10.26493/1855-3974.1525.7f3
LA  - en
ID  - 10_26493_1855_3974_1525_7f3
ER  - 
%0 Journal Article
%A Michael A. Henning
%A Iztok Peterin
%T A characterization of graphs with disjoint total dominating sets
	
%J Ars mathematica contemporanea
%D 2019
%P 359-375
%V 16
%N 2
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1525.7f3/
%R 10.26493/1855-3974.1525.7f3
%G en
%F 10_26493_1855_3974_1525_7f3
Michael A. Henning; Iztok Peterin. A characterization of graphs with disjoint total dominating sets. Ars mathematica contemporanea, Tome 16 (2019) no. 2, pp. 359-375. doi: 10.26493/1855-3974.1525.7f3

Cité par Sources :