A Note on the Locating-Total Domination in Graphs

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.

Bibliographic Details
Main Authors:	Miller Mirka, Rajan R. Sundara, Jayagopal R., Rajasingh Indra, Manuel Paul
Format:	Article
Language:	English
Published:	Sciendo 2017-08-01
Series:	Discussiones Mathematicae Graph Theory
Subjects:	dominating set total dominating set locating-dominating set locating-total dominating set regular graphs 05c69
Online Access:	https://doi.org/10.7151/dmgt.1961

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spelling	doaj-e89aec8a8c9141fa9e27822be73726372021-09-05T17:20:22ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922017-08-0137374575410.7151/dmgt.1961dmgt.1961A Note on the Locating-Total Domination in GraphsMiller Mirka0Rajan R. Sundara1Jayagopal R.2Rajasingh Indra3Manuel Paul4School of Mathematical and Physical Sciences, University of Newcastle, Australia; Department of Mathematics, University of West Bohemia, Pilsen, Czech RepublicDepartment of Mathematics, Anna University, Chennai-600 025, IndiaSchool of Advanced Sciences, VIT University, Chennai-600 127, IndiaSchool of Advanced Sciences, VIT University, Chennai-600 127, IndiaDepartment of Information Science, Kuwait University, Safat, KuwaitIn 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.https://doi.org/10.7151/dmgt.1961dominating settotal dominating setlocating-dominating setlocating-total dominating setregular graphs05c69
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Miller Mirka Rajan R. Sundara Jayagopal R. Rajasingh Indra Manuel Paul
spellingShingle	Miller Mirka Rajan R. Sundara Jayagopal R. Rajasingh Indra Manuel Paul A Note on the Locating-Total Domination in Graphs Discussiones Mathematicae Graph Theory dominating set total dominating set locating-dominating set locating-total dominating set regular graphs 05c69
author_facet	Miller Mirka Rajan R. Sundara Jayagopal R. Rajasingh Indra Manuel Paul
author_sort	Miller Mirka
title	A Note on the Locating-Total Domination in Graphs
title_short	A Note on the Locating-Total Domination in Graphs
title_full	A Note on the Locating-Total Domination in Graphs
title_fullStr	A Note on the Locating-Total Domination in Graphs
title_full_unstemmed	A Note on the Locating-Total Domination in Graphs
title_sort	note on the locating-total domination in graphs
publisher	Sciendo
series	Discussiones Mathematicae Graph Theory
issn	2083-5892
publishDate	2017-08-01
description	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.
topic	dominating set total dominating set locating-dominating set locating-total dominating set regular graphs 05c69
url	https://doi.org/10.7151/dmgt.1961
work_keys_str_mv	AT millermirka anoteonthelocatingtotaldominationingraphs AT rajanrsundara anoteonthelocatingtotaldominationingraphs AT jayagopalr anoteonthelocatingtotaldominationingraphs AT rajasinghindra anoteonthelocatingtotaldominationingraphs AT manuelpaul anoteonthelocatingtotaldominationingraphs AT millermirka noteonthelocatingtotaldominationingraphs AT rajanrsundara noteonthelocatingtotaldominationingraphs AT jayagopalr noteonthelocatingtotaldominationingraphs AT rajasinghindra noteonthelocatingtotaldominationingraphs AT manuelpaul noteonthelocatingtotaldominationingraphs
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A Note on the Locating-Total Domination in Graphs

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