Algorithmic aspects of total k-subdomination in graphs

Abstract

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 assigned to the vertices under f. In this paper, we present a cubic time algorithm to compute the total k-subdomination number of a tree and also show that the associated decision problem is NP-complete for general graphs.

Subdomination in Graphs with Upper-Bounded Vertex Degree

“…A number of additional inequalities related to majority domination and k-subdomination can be found in [10]. For other results applicable to regular and nearly regular graphs with some variations of the majority domination and k-subdomination models we refer to [20][21][22][23][24][25][26][27][28].…”

Global signed total domination in graphs

“…Note that G admits a STDF if and only if G has no isolated vertices. The signed total domination number of G, denoted by γ st (G), is the minimum weight of a signed total dominating function of G. The signed total domination number has been studied by several authors (see for example [1], [2], [4], [6]).…”

Minus total k-subdomination in graphs

“…For k ∈ Z + , 1 k |V |, a function f : V → {−1, 0, 1} is said to be an MTkSF on G in [5] if f (N (v)) 1 for at least k vertices v in G.…”