Limited Dominating Broadcast in Graphs

Abstract

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.

Dominating 2-broadcast in graphs: Complexity, bounds and extremal graphs

“…We begin this section with the formal definition of dominating 2-broadcast, following the ideas proposed in [7]. To our knowledge, this concept has not previously been studied, except in [16] where some straightforward properties are introduced.…”

General bounds on limited broadcast domination

“…First of all, we present the formal definition that was suggested in [6] as an open problem in order to provide a model that could better reflect the real world situation of a transmitter network with antennas of limited power. This concept has been studied in the in [2,13] for the case k = 2.…”