In this paper we obtain a sharp (improved) lower bound on the locatingtotal domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.

Jayagopal R

Mathematics

School of Advanced Sciences

Chennai Campus

Indra Rajasingh

Miller M

Rajan R.S

Manuel P.

Fulltext

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Discussiones Mathematicae Graph Theory

A locating-dominating set (LDS) of a graph G is a dominating set S of G such that for every two vertices u and v in V(G)∖S, N(u)∩S≠N(v)∩S. The locating-domination number γL(G) is the minimum cardinality of a LDS of G. Further if S is a total dominating set then S is called a locating-total dominating set. In this paper we determine the domination, total domination, locating-domination and locating-total domination numbers for hypertrees and sibling trees. © 2020 Elsevier B.V.

Discrete Applied Mathematics

Domination parameters in hypertrees and sibling trees

A note on the locating-total domination in graphs

Journal	Discussiones Mathematicae Graph Theory
Publisher	Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora
ISSN	1234-3099
Open Access	0