The restrained rainbow bondage number of a graph

Abstract

Abstract.A restrained k-rainbow dominating function (RkRDF) of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2, . . . , k} such that forThe minimum weight of a restrained k-rainbow dominating function of G is called the restrained k-rainbow domination number of G, denoted by γ r r k (G). The restrained krainbow bondage number b r r k (G) of a graph G with maximum degree at least two is the minimum cardinality of all sets F ⊆ E (G) for which γ r r k (G − F ) > γ r r k (G). In this paper, we initiate the study of the restrained k-rainbow bondage number in graphs and we present some sharp bounds for b r r 2 (G). In addition, we determine the restrained 2-rainbow bondage number of some classes of graphs.