The complete cototal domination set is said to be irredundant dominating if for each u ∈ S, NG [S − {u}] ≠ [S]. minimum cardinality taken over all an called number and denoted by γircc(G). Here a new parameter was introduced the study of bounds γircc(G) initiated.

Let k ≥ 1 be an integer and G a graph of minimum degree δ ( ) − 1. A set D ⊆ V is said to -tuple dominating if | N [ v ] ∩ for every vertex ∈ ), where represents the closed neighbourhood . The cardinality among all sets domination number In this paper, we continue with study classical parameter in graphs. particular, provide some relationships that exist between other parameters, like multiple ...

A set $S subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ andevery vertex in $S$ is within distance 2 of another vertex of $S$. Thesemitotal domination number $gamma_{t2}(G)$ is the minimumcardinality of a semitotal dominating set of $G$.We show that the semitotal domination problem isAPX-complete for bounded-degree graphs, and the semitotal dominatio...

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...

We provide tight hardness results and approxiamation algorithms for many existing domination problems. We start with the positive influence dominating set (PIDS) problem, originated from the context of influence propagation in social networks. The PIDS problem seeks for a minimal set of nodes P such that all other nodes in the network have at least a fraction ρ > 0 of their neighbors in P; in t...