Abstract
An independent broadcast on a connected graph G is a function f:V(G)→N0 such that, for every vertex x of G, the value f(x) is at most the eccentricity of x in G, and f(x)>0 implies that f(y)=0 for every vertex y of G within distance at most f(x) from x. The broadcast independence number αb(G) of G is the largest weight ∑x∈V(G)f(x) of an independent broadcast f on G. Clearly, αb(G) is at least the independence number α(G) for every connected graph G. Our main result implies αb(G)≤4α(G). We prove a tight inequality and characterize all extremal graphs.
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