Minus k-subdomination in graphs II

Minus edge k-subdomination numbers in graphs

The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end-vertex with e. Let f be a function on E(G), the edge set of G, into the set {−1, 0, 1}. If ∑ x∈N [e] f(x) ≥ 1 for at least k edges e of G, then f is called a minus edge k-subdominating function of G. The minimum of the values ∑ e∈E(G) f(e), taken over all minus edge k-subdomin...

Minus k-subdomination in graphs III

Let G = (V, E) be a graph. For any real valued function 1 : V --+ R and S ~ V, let 1 (S) = L:UES 1 ( u). The weight of 1 is defined as I(V). We will also denote I(N[v]) by I[v]' where v E V. A minus k-subdominating function (k8F) for G is defined in [1] as a function 1 : V --+ {-I, 0, I} such that I[v] 2:: 1 for at least k vertices of G. The minus k-subdomination number of a graph G, denoted by...

Algorithmic aspects of minus total k-subdomination in graphs

k-Subdomination in graphs

For a positive integer k, a k-subdominating function of a graph G=(V; E) is a function f :V →{−1; 1} such that ∑u∈NG [v] f(u)¿ 1 for at least k vertices v of G. The ksubdomination number of G, denoted by ks(G), is the minimum of ∑ v∈V f(v) taken over all k-subdominating functions f of G. In this article, we prove a conjecture for k-subdomination on trees proposed by Cockayne and Mynhardt. We al...

The minus k-domination numbers in graphs

For any integer  ‎, ‎a minus  k-dominating function is a‎function  f‎ : ‎V (G)  {-1,0‎, ‎1} satisfying w) for every  vertex v, ‎where N(v) ={u V(G) | uv  E(G)}  and N[v] =N(v)cup {v}. ‎The minimum of ‎the values of  v)‎, ‎taken over all minus‎k-dominating functions f,‎ is called the minus k-domination‎number and is denoted by $gamma_k^-(G)$ ‎. ‎In this paper‎, ‎we ‎introduce the study of minu...