Majority domination in graphs

Strict majority functions on graphs

“…We obtain a strict majority function of weight For the weak majority number, the formula of Proposition 6 also holds when n = m ≥ 2 (see [3]). Hence we have the following corollary of Proposition 5 which serves to illustrate that the strict majority number and the weak majority number of a graph may differ by an arbitrarily large amount.…”

“…Since all vertices of a clique have the same closed neighborhood, the strong or weak (see [3]) majority number of a complete graph K n is the minimum excess of positive over negative opinions. Thus Proposition 1.…”

“…The signed domination number of G is the minimum weight of a signed dominating function on G. A majority dominating function [7] is an opinion function for which at least half the vertices vote aye, and the minimum weight of such a function is the majority domination number. The majority dominating function was studied in [3]. To avoid confusion, in this paper we use weak majority function in place of majority dominating function, and weak majority number in place of majority domination number.…”

“…A global decision requires more than half of the votes. This topic was first studied in [3] using the model that a global decision requires at least half of the votes.…”

“…Our definitions are based on those defined in [2,3,6,7]. A signed dominating function [6] is an opinion function such that the sum of the opinions in each closed neighborhood is positive (every vertex votes aye).…”