Trees with equal broadcast and domination numbers
Date
2011-12-19
Authors
Lunney, Scott
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Abstract
A broadcast on a graph G=(V,E) is a function f : V → {0, ..., diam(G)} that assigns an integer value
to each vertex such that, for each v ∈ V , f (v) ≤ e(v), the eccentricity of v. The broadcast number of a graph is the minimum value of Σv∈V f (v) among all broadcasts f with the property that for each vertex x of V, f (v) ≥ d(x, v) for some vertex v having positive f (v). This number is bounded above by both the radius of the graph and its domination number. Graphs for which the broadcast number is equal to the domination number are called 1-cap graphs. We investigate and characterize a class
of 1-cap trees.
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Keywords
Broadcasts in Graphs, Dominating Broadcasts