LIMITED DOMINATING BROADCAST IN GRAPHS

For a given graph G, a function f : V (G) ! f0; 1; :::; diam Gg such that for every vertex v of G, f(v) · e(v) (where e(v) is the eccentricity of the vertex v and diamG is the diameter of G), is a broadcast on G. A broadcast f is a dominating broadcast if and only if Nf [V +] = V (G), where V + = fujf(u) > 0g, Nf [u] = fvjd(u; v) · f(u)g is the broadcast neighborhood of u and Nf [V ] = [u2V Nf [u]. In this paper we settle a question posed by Dunbar et al. [3], and obtain some new results concerning limited dominating broadcasts in graphs.