Geodesic
A Note on the Locating-Total Domination in Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 745-754.

Voir la notice de l'article provenant de la source Library of Science

In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Keywords: dominating set, total dominating set, locating-dominating set, locating-total dominating set, regular graphs 
@article{DMGT_2017_37_3_a16,
     author = {Miller, Mirka and Rajan, R. Sundara and Jayagopal, R. and Rajasingh, Indra and Manuel, Paul},
     title = {A {Note} on the {Locating-Total} {Domination} in {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {745--754},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a16/}
}
TY  - JOUR
AU  - Miller, Mirka
AU  - Rajan, R. Sundara
AU  - Jayagopal, R.
AU  - Rajasingh, Indra
AU  - Manuel, Paul
TI  - A Note on the Locating-Total Domination in Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 745
EP  - 754
VL  - 37
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a16/
LA  - en
ID  - DMGT_2017_37_3_a16
ER  - 
%0 Journal Article
%A Miller, Mirka
%A Rajan, R. Sundara
%A Jayagopal, R.
%A Rajasingh, Indra
%A Manuel, Paul
%T A Note on the Locating-Total Domination in Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 745-754
%V 37
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a16/
%G en
%F DMGT_2017_37_3_a16
Miller, Mirka; Rajan, R. Sundara; Jayagopal, R.; Rajasingh, Indra; Manuel, Paul. A Note on the Locating-Total Domination in Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 745-754. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a16/

[1] I. Charon, O. Hudry and A. Lobstein, Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard, Theoret. Comput. Sci. 290 (2003) 2109–2120. doi:10.1016/S0304-3975(02)00536-4

[2] M. Chellali, On Locating and differentiating-total domination in trees, Discuss. Math. Graph Theory 28 (2008) 383–392. doi:10.7151/dmgt.1414

[3] X. Chen and M.Y. Sohn, Bounds on the locating-total domination number of a tree, Discrete Appl. Math. 159 (2011) 769–773. doi:10.1016/j.dam.2010.12.025

[4] J.-F. Fang, The bipancycle-connectivity of the hypercube, Inform. Sci. 178 (2008) 4679–4687.

[5] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman & Company Publisher, San Francisco, US, 1979).

[6] T.W. Haynes, M.A. Henning and J. Howard, Locating and total dominating sets in trees, Discrete Appl. Math. 154 (2006) 1293–1300. doi:10.1016/j.dam.2006.01.002

[7] M.A. Henning and C. Löwenstein, Locating-total domination in claw-free cubic graphs, Discrete Math. 312 (2012) 3107–3116. doi:10.1016/j.disc.2012.06.024

[8] M.A. Henning and N.J. Rad, Locating-total domination in graphs, Discrete Appl. Math. 160 (2012) 1986–1993. doi:10.1016/j.dam.2012.04.004

[9] H. Hosoya and F. Harary, On the matching properties of three fence graphs, J. Math. Chem. 12 (1993) 211–218. doi:10.1007/BF01164636

[10] B.N. Omamalin, Locating total dominating sets in the join, corona and composition of graphs, Appl. Math. Sci. 8 (2014) 2363–2374. doi:10.12988/ams.2014.43205

[11] P.J. Slater, Fault-tolerant locating-dominating sets, Discrete Math. 249 (2002) 179–189. doi:10.1016/S0012-365X(01)00244-8

[12] J. Xu, Topological Structure and Analysis of Interconnection Networks (Kluwer Academic Publishers, London, UK, 2001). doi:10.1007/978-1-4757-3387-7