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We say that a function f : V → {0, 1,. .. , diam(G)} is a broadcast if for every vertex 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) = Σ v∈V f (v). In this paper we introduce and study the minimum and maximum costs of several types of broadcasts in graphs,… (More)

An e = 1 function is a function f : V (G) → [0, 1] such that every non-isolated vertex u is adjacent to some vertex v such that f (u) + f (v) = 1, and every isolated vertex w has f (w) = 1. A theory of e = 1 functions is developed focussing on minimal and maximal e = 1 functions. Relationships are traced between e = 1 parameters and some well-known… (More)

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