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

• Autorzy: Mustapha Chellali , Nader Jafari Rad
• 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).

Słowa kluczowe

EN

Roman domination; independent Roman domination; strong equality; trees

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 337-346

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

Mustapha Chellali

• LAMDA-RO, Department of Mathematics University of Blida B.P. 270, Blida, Algeria

autor

Nader Jafari Rad

• 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

Bibliografia

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• [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.

Identyfikatory

DOI

10.7151/dmgt.1669