1 research outputs found
Roman domination and Mycieleki's structure in graphs
For a graph , a function is called Roman
dominating function (RDF) if for any vertex with , there is at
least one vertex in its neighborhood with . The weight of an RDF
of is the value . The minimum weight of an RDF
of is its Roman domination number and denoted by . In this
paper, we first show that , where is the Mycielekian graph of , and then
characterize the graphs achieving equality in these bounds. Then for any
positive integer , we compute the Roman domination number of the
-Mycieleskian of a special Roman graph in terms on
. Finally we present several graphs to illustrate the discussed
graphs