Lower Bounds on the Majority Domination Number of Graphs

Let G=(V,E) be a simple graph. For any real valued function f∶V→R and SV, let f(S)=∑ u∈S?f(u). A majority dominating function is a function f∶V→-1,1 such that f(N)≥1 for at least half the vertices v∈V. Then majority domination number of a graph G is γ maj(G)=minf(V)|f is a majority dominating function on G. We obtain lower bounds on this parameter and generalize some results of Henning.