Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 455-462
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A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S. A dominating set S is a locating-dominating set of G if every two vertices x, y ∈ V − S satisfy N(x) ∩ S N(y) ∩ S. The locating-domination number γ_L (G) is the minimum cardinality of a locating-dominating set of G. A total dominating set S is called a differentiating-total dominating set if for every pair of distinct vertices u and v of G, N[u] ∩ S N[v] ∩ S. The minimum cardinality of a differentiating-total dominating set of G is the differentiating-total domination number of G, denoted by γ_t^D (G). We obtain new upper bounds for the locating-domination number, and the differentiating-total domination number in trees. Moreover, we characterize all trees achieving equality for the new bounds.
Keywords:
locating-dominating set, differentiating-total dominating set, tree
@article{DMGT_2018_38_2_a8,
author = {Rad, Nader Jafari and Rahbani, Hadi},
title = {Bounds on the {Locating-Domination} {Number} and {Differentiating-Total} {Domination} {Number} in {Trees}},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {455--462},
publisher = {mathdoc},
volume = {38},
number = {2},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a8/}
}
TY - JOUR AU - Rad, Nader Jafari AU - Rahbani, Hadi TI - Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees JO - Discussiones Mathematicae. Graph Theory PY - 2018 SP - 455 EP - 462 VL - 38 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a8/ LA - en ID - DMGT_2018_38_2_a8 ER -
%0 Journal Article %A Rad, Nader Jafari %A Rahbani, Hadi %T Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees %J Discussiones Mathematicae. Graph Theory %D 2018 %P 455-462 %V 38 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a8/ %G en %F DMGT_2018_38_2_a8
Rad, Nader Jafari; Rahbani, Hadi. Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 455-462. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a8/