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2013 | 33 | 2 | 337-346
Tytuł artykułu

Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A Roman dominating function (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 is the value f(V (G)) = P u2V (G) f(u). An RDF f in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number R(G) (respectively, the independent Roman domination number iR(G)) is the minimum weight of an RDF (respectively, independent RDF) on G. We say that R(G) strongly equals iR(G), denoted by R(G) ≡ iR(G), if every RDF on G of minimum weight is independent. In this paper we provide a constructive characterization of trees T with R(T) ≡ iR(T).
Wydawca
Rocznik
Tom
33
Numer
2
Strony
337-346
Opis fizyczny
Daty
wydano
2013-05-01
online
2013-04-13
Twórcy
  • LAMDA-RO, Department of Mathematics University of Blida B.P. 270, Blida, Algeria, mchellali@hotmail.com
  • Department of Mathematics, Shahrood University of Technology Shahrood, Iran and School of Mathematics Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran, n.jafarirad@gmail
Bibliografia
  • [1] E.J. Cockayne, P.A. Dreyer Jr., S.M. Hedetniemi and S.T. Hedetniemi, On Roman domination in graphs, Discrete Math. 278 (2004) 11-22. doi:10.1016/j.disc.2003.06.004[Crossref]
  • [2] T.W. Haynes, M.A. Henning and P.J. Slater, Strong equality of domination parameters in trees, Discrete Math. 260 (2003) 77-87. doi:10.1016/S0012-365X(02)00451-X[Crossref]
  • [3] T.W. Haynes, M.A. Henning and P.J. Slater, Strong equality of upper domination and independence in trees, Util. Math. 59 (2001) 111-124.
  • [4] T.W. Haynes and P.J. Slater, Paired-domination in graphs, Networks 32 (1998) 199-206. doi:10.1002/(SICI)1097-0037(199810)32:3h199::AID-NET4i3.0.CO;2-F[Crossref]
  • [5] M.A. Henning, A characterization of Roman trees, Discuss. Math. Graph Theory 22 (2002) 325-334. doi:10.7151/dmgt.1178[Crossref]
  • [6] M.A. Henning, Defending the Roman Empire from multiple attacks, Discrete Math. 271 (2003) 101-115. doi:10.1016/S0012-365X(03)00040-2[Crossref]
  • [7] N. Jafari Rad and L. Volkmann, Changing and unchanging the Roman domination number of a graph, Util. Math. 89 (2012) 79-95.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1669
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