Mixed Roman Domination in Graphs
Document Type
Article
Publication Date
10-1-2017
Description
Let G= (V, E) be a simple graph with vertex set V and edge set E. A mixed Roman dominating function (MRDF) of G is a function f: V∪ E→ { 0 , 1 , 2 } satisfying the condition every element x∈ V∪ E for which f(x) = 0 is adjacent or incident to at least one element y∈ V∪ E for which f(y) = 2. The weight of a MRDF f is ω(f) = ∑ x∈V∪Ef(x). The mixed Roman domination number of G is the minimum weight of a mixed Roman dominating function of G. In this paper, we initiate the study of the mixed Roman domination number and we present bounds for this parameter. We characterize the graphs attaining an upper bound and the graphs having small mixed Roman domination numbers.
Citation Information
Ahangar, H. Abdollahzadeh; Haynes, Teresa W.; and Valenzuela-Tripodoro, J. C.. 2017. Mixed Roman Domination in Graphs. Bulletin of the Malaysian Mathematical Sciences Society. Vol.40(4). 1443-1454. https://doi.org/10.1007/s40840-015-0141-1 ISSN: 0126-6705