Broadcasts in graphs

Authors:
Jean E. Dunbar;David J. Erwin;Teresa W. Haynes;Sandra M. Hedetniemi;Stephen T. Hedetniemi
Affiliations:
Converse College, Spartanburg, SC;Trinity College, Hartford, CT;East Tennessee State University, Johnson City, TN;Clemson University, Clemson, SC;Clemson University, Clemson, SC
Venue:
Discrete Applied Mathematics
Year:
2006

Citing 1
Cited 1

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Abstract

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) = Σv∈V f(v). In this paper we introduce and study the minimum and maximum costs of several types of broadcasts in graphs, including dominating, independent and efficient broadcasts.