Global dominating broadcast in graphs.

A broadcast on a graph G = (V , E) is a function f : V → { 0 , 1 , ... , diam (G) } such that for each v ∈ V , f (v) ≤ e (v) , where diam (G) denotes the diameter of G and e (v) denotes the eccentricity of v. The cost of a broadcast is the value f (V) = ∑ v ∈ V f (v). In this paper, we define and study a new invariant of broadcasts in graphs, which is global dominating broadcast. A dominating broadcast f of a graph G is a global dominating broadcast if f is also a dominating broadcast of G ¯ the complement of G. We begin by determining the global broadcast domination number of bipartite graphs, paths, cycles, grid graphs and trees. Then we establish lower and upper bounds on the global broadcast domination number of a graph. Finally, we establish relationships between the global broadcast domination number and other parameters. [ABSTRACT FROM AUTHOR]