|
Abstract
|
A 2-rainbow dominating function (2RDF) on a graph G = (V;E)
is a function f from the vertex set V to the set of all subsets of the
set f1; 2g such that for any vertex v 2 V with f(v) = ; the condition
[u2N(v)f(u) = f1; 2g is ful lled. The weight of a 2RDF f is the value
!(f) =
P
v2V (G) jf(v)j. The 2-rainbow domination number, denoted
by r2(G), is the minimum weight of a 2RDF on G. The rainbow
bondage number br2(G) of a graph G with maximum degree at least
two, is the minimum cardinality of all sets E0 E(G) for which
r2(G E0) > r2(G). Dehgardi, Sheikholeslami and Volkmann,
[Discrete Appl. Math. 174 (2014), 133-139] proved that the rainbow
bondage number of a planar graph does not exceed 15. In this paper
we improve this result.
|