k-Subdomination in graphs

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...

Signed 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, 1}. If ∑ x∈N [e] f(x) ≥ 1 for at least k edges e of G, then f is called a signed edge k-subdominating function of G. The minimum of the values ∑ e∈E(G) f(e), taken over all signed edge k-subdomina...

Signed star k-subdomination numbers in graphs

Let G be a simple graph without isolated vertex with vertex set V (G) and edge set E(G). A function f : E(G) −→ {−1, 1} is said to be a signed star k-subdominating function of G if ∑ e∈E(v) f (e) ≥ 1 for at least k vertices v of G, where E(v) = {uv ∈ E(G) | u ∈ N (v)}. The value min ∑ e∈E(G) f (e), taking over all signed star k-subdominating function f of G is called the signed star k-subdomina...

Algorithmic aspects of total k-subdomination in graphs

Let G = (V, E) be a graph and let k ∈ Z. A total k-subdominating function is a function f : V → {−1, 1} such that for at least k vertices v of G, the sum of the function values of f in the open neighborhood of v is positive. The total k-subdomination number of G is the minimum value of f(V ) over all total k-subdominating functions f of G where f(V ) denotes the sum of the function values assig...

Algorithmic aspects of minus total k-subdomination in graphs

A note on signed and minus domination in graphs

In this paper, we give upper bounds on the upper signed domination number of [l, k] graphs, which generalize some results obtained in other papers. Further, good lower bounds are established for the minus ksubdomination number γ−101 ks and signed k-subdomination number γ −11 ks .