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 ...

Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the numbe...

Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set. The problems of finding the minimum size of a k-dominating, resp. total k-d...