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Abstract
A Roman dominating function on a graph G=(V,E) is defined to be 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. A dominating set D⊆V is a weakly connected dominating set of G if the graph (V,E∩(D×V)) is connected. We define a weakly connected Roman dominating function on a graph G to be a Roman dominating function such that the set {u ∈ V : f(u) ∈{1,2}} is a weakly connected dominating set of G. The weight of a weakly connected Roman dominating function is the value f(V) =∑u∈V f(u). The minimum weight of a weakly connected Roman dominating function on a graph G is called the weakly connected Roman domination number of G and is denoted by γ wc R (G). In this paper, we initiate the study of this parameter.
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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DISCRETE APPLIED MATHEMATICS
no. 267,
pages 151 - 159,
ISSN: 0166-218X - Language:
- English
- Publication year:
- 2019
- Bibliographic description:
- Raczek J., Cyman J.: Weakly connected Roman domination in graphs// DISCRETE APPLIED MATHEMATICS -Vol. 267, (2019), s.151-159
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.dam.2019.05.002
- Verified by:
- Gdańsk University of Technology
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