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NOTES ON DOUBLE ROMAN DOMINATION EDGE CRITICAL GRAPHS
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Given a graph G=(V,E), a double Roman dominating function (DRDF) on a graphs a function:V →{0, 1, 2, 3}satisfying the condition that every vertex u for which(u)=0 is adjacent to at least one vertex v for which f(v) = 3 or two vertices v1 and v2 for which f(v1)=f(v2) = 2, and every vertex for which f(u) = 1 is adjacent to at least one vertex v for which f(v) ≥ 2. Theweight w(f) of a double Roman dominating function f is the value w(f)=∑_(u∈V) f(u). The minimum weight of a double Roman dominating function on a graph G is called the double Roman domination number of G, denoted by γdR(G). We say that G is k-γdR-edge critical, if γdR(G+e) <γdR(G) for each e∈E(G), where G is the complement of G, and k-γdR-edge supercritical if γdR(G)=k anddR(G+e)=γdR(G)−2 for every edge e∈E(G). In this paper, we characterize γdR-edge critical trees, answering a problem posed by Nazari-Moghaddam and Volkmann (Discrete Math. Algorithms App. 12 (2020) 2050020). Moreover, we investigate connected-γdR-edge supercritical graphs for k∈{5, 6, 7, 8}. Mathematics Sub ject Classiifcation. 05C69.
Double Roman dominationedge critical treeedge supercritical graphs
ABDELHAK OMAR、AHMED BOUCHOU
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LAMDA-RO Laboratory, Department of Mathematics, University of Blida 1, Blida, Algeria
LAMDA-RO Laboratory, Department of Mathematics, University of Blida 1, Blida, Algeria||University of Medea, Medea, Algeria
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Edp Sciences S A
