Authors: L. Volkmann Title: The double Roman domatic number of a digraph Source: Discussiones Mathematicae Graph Theory Received 08.03.2018, Revised 15.06.2018, Accepted 15.06.2018, doi: 10.7151/dmgt.2161 | |
Abstract: A double Roman dominating function on a digraph D with vertex set V(D) is defined in {[G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).]} as a function f:V(D)→{0,1,2,3} having the property that if f(v)=0, then the vertex v must have at least two in-neighbors assigned 2 under f or one in-neighbor w with f(w)=3, and if f(v)=1, then the vertex v must have at least one in-neighbor u with f(u)≥ 2. A set {f_{1},f_{2},...,f_{d}} of distinct double Roman dominating functions on D with the property that ∑_{i=1}^{d}f_{i}(v)\le 3 for each v∈V(D) is called a double Roman dominating family (of functions) on D. The maximum number of functions in a double Roman dominating family on D is the double Roman domatic number of D, denoted by d_{dR}(D). We initiate the study of the double Roman domatic number, and we present different sharp bounds on d_{dR}(D). In addition, we determine the double Roman domatic number of some classes of digraphs. | |
Keywords: digraph, double Roman domination, double Roman domatic number | |
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