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.
The second and the third authors were partially supported by NSERC of Canada. The second author was supported also by the National Science Council of Taiwan under grant NSC 93-2811-M-002-004. The first author is the corresponding author.
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Liedloff, M., Kloks, T., Liu, J., Peng, SL. (2005). Roman Domination over Some Graph Classes. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_10
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DOI: https://doi.org/10.1007/11604686_10
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