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Roman Domination over Some Graph Classes

  • Mathieu Liedloff
  • Ton Kloks
  • Jiping Liu
  • Sheng-Lung Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3787)

Abstract

A Roman dominating function of a graph G = (V,E) is a function f : V → {0,1,2} such that every vertex x with f(x) = 0 is adjacent to at least one vertex y with f(y) = 2. The weight of a Roman dominating function is defined to be f(V) = ∑ x ∈ V f(x), and the minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G.

In this paper we answer an open problem mentioned in [2] by showing that the Roman domination number of an interval graph can be computed in linear time. We also show that the Roman domination number of a cograph can be computed in linear time. Besides, we show that there are polynomial time algorithms for computing the Roman domination numbers of AT-free graphs and graphs with a d-octopus.

Keywords

Time Algorithm Discrete Math Interval Graph Domination Number Linear Time Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Mathieu Liedloff
    • 1
  • Ton Kloks
    • 1
  • Jiping Liu
    • 2
  • Sheng-Lung Peng
    • 3
  1. 1.Laboratoire d’Informatique Théorique et AppliquéeUniversité Paul Verlaine – MetzMetzFrance
  2. 2.Department of Mathematics and Computer ScienceThe university of LethbridgeAlbertaCanada
  3. 3.Department of Computer Science and Information EngineeringNational Dong Hwa UniversityHualienTaiwan, R.O.C

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