Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that different vertices can be assigned different domination powers. Broadcast domination assigns an integer power f(v) ≥ 0 to each vertex v of a given graph, such that every vertex of the graph is within distance f(v) from some vertex v having f(v) ≥ 1. The optimal broadcast d...

This paper is motivated by the concept of nonnegative signed domination that was introduced by Huang, Li, and Feng in 2013 [15]. We study the non-negative signed domination problem from the theoretical point of view. For networks modeled by strongly chordal graphs and distance-hereditary graphs, we show that the non-negative signed domination problem can be solved in polynomial time. For networ...

Abstract: Let G = (VG, EG) be a simple connected graph. The eccentric distance sum of G is defined as ξ(G) = ∑ v∈VG εG(v)DG(v), where εG(v) is the eccentricity of the vertex v and DG(v) = ∑ u∈VG dG(u, v) is the sum of all distances from the vertex v. In this paper the tree among n-vertex trees with domination number γ having the minimal eccentric distance sum is determined and the tree among n-...

Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that vertices can be assigned various domination powers. Broadcast domination assigns a power f(v) 0 to each vertex v of a given graph, such that every vertex of the graph is within distance f(v) from some vertex v having f(v) 1. The optimal broadcast domination problem seeks t...

Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v) > 0. We can regard the vertices v with f(v) > 0 as broadcast stations, each having a transmission power that might be di erent from the powers of other stations. The optimal broadcast domination problem seeks to minimize...

The broadcast domination problem of a graph G = (V,E) is to find a subset B ⊆ V such that the vertices in V \B can be dominated by some vertex in B. The difference between broadcast domination and classical domination is that each vertex v in B is assigned a power value f(v) where f(v) ≥ 1 and the vertices in distance at most f(v) to v can hear (be dominated by) v. The goal is to find the minim...