ABSTRACT
For any real valued function f : V → R and S ⊆ V, let f(S) = Σu∊s f(u). The weight of f is defined as f(V). We will also denote f(N[v]) by f[v], where v ∊ V. A minus dominating function is defined in [6] as a function f : V → { –1,0, 1} such that f[v] ≥ 1 for every v ∊ V. The minus domination number of a graph G is γ–(G) = min { f(V) | f is a minus dominating function on G}. A signed dominating function is defined in [7] as a function f : V → { – 1, 1} such that f[v] ≥ 1 for every v ∊ V. The signed domination number of a graph G is γ s (G) = min{f(V) | f is a signed dominating function on G}. A majority dominating function is defined in [3] as a function f : V → { – 1, 1} such that f[v] ≥ 1 for at least half the vertices v ∊ V. The majority domination number of a graph G is γ maj(G) = min {f(V) | f is a majority dominating function of G}. Let k; be a positive integer such that 1 ≤ k ≤ |V|. A signed k-subdominating function (kSF) for G is defined in [4] as a function f : V → { – 1, 1} such that f[v] ≥ 1 for at least k vertices of G. The signed k-subdomination number of a graph G is γ–11 ks ) = min{f(V) | f is a signed kSF of G}. In the special cases where k = |V| and k = ⌈ | V | 2 ⌉ , γ k s − 11 ( G ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141428/0b8b6f32-6ee7-486d-b7f9-109dc1ca019f/content/eqn91_2.tif"/> is, respectively, the signed domination 92number and the majority domination number.
