Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
A Roman dominating function (or just RDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF f is the value f(V (G)) = ∑u∈V(G) f(u). An RDF f can be represented as f = (V0, V1, V2), where Vi = {v ∈ V : f(v) = i} for i = 0, 1, 2. An RDF f = (V0, V1, V2) is called a locating Roman dominating function (or just LRDF) if N(u) ∩ V2 ≠ N(v) ∩ V2 for any pair u, v of distinct vertices of V0. The locating Roman domination number [...] γRL(G) $\gamma _R^L (G)$ is the minimum weight of an LRDF of G. In this paper, we study the locating Roman domination number in trees. We obtain lower and upper bounds for the locating Roman domination number of a tree in terms of its order and the number of leaves and support vertices, and characterize trees achieving equality for the bounds.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
49-62
Opis fizyczny
Daty
wydano
2018-02-01
otrzymano
2016-01-07
poprawiono
2016-09-21
zaakceptowano
2016-09-21
online
2017-12-30
Twórcy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1989