LIMITED DOMINATING BROADCAST IN GRAPHS
Nader Jafari Rad, Fatemeh Khosravi · Discrete Mathematics Algorithms and Applications · 2013
For a given graph G, a function f : V(G) → {0, 1, …, diamG} 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 Nf[V+] = V(G), where V+ = {u | f(u) > 0}, Nf[V+] = ⋃u∈V+Nf[u], and Nf[u] = {v | d(u, v) ≤ f(u)}. In this paper, inspired by Dunbar et al. [3], we study limited dominating broadcast in graphs and obtain some properties, bounds, and characterizations for limited broadcast domination number in graphs.