Abstract In 1985, Fink and Jacobson gave a generalization of the concepts of domination
and independence in graphs. For a positive integer k, a subset S of vertices in a graph G=(V …

In 2008, Hedetniemi et al. introduced the concept of (1, k)‐domination and obtained some
interesting results for (1, 2)‐domination. Obviously every (1, 1)‐dominating set of a graph …

The k-domination number of a graph is the cardinality of a smallest set of vertices such that
every vertex not in the set is adjacent to at least k vertices of the set. We prove two bounds …

Let G be a graph and let D be a subset of its vertex set. D is called k-dominating if| N (v)∩
D|≥ k for all v∈ V (G)∖ D; D is called k-tuple dominating if| N v∩ D|≥ k for all v∈ V (G); and …

The k-domination number γk (G) of a simple, undirected graph G is the order of a smallest
subset D of the vertices of G such that each vertex of G is either in D or adjacent to at least k …

We initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent
dominating set of a graph G is a set D of vertices of G such that every vertex of V (G) ∖ DV …

The system is fault-tolerant if, in the case that just one of the previously employed units fails,
a different chain of units is utilised in its place. Because they provide the best fault tolerance …

A subset S of vertices of a graph G is k-dominating if every vertex not in S has at least k
neighbours in S. The k-domination number γ k (G) is the minimum cardinality of ak …

A set S of vertices in a graph G is a 2-dominating set if every vertex of G not in S is adjacent
to at least two vertices in S, and S is a 2-independent set if every vertex in S is adjacent to at …

A vertex of a graph is said to dominate itself and all of its neighbors. A subset D⊆ V (G) is a
2-dominating set of G if every vertex of V (G)\D is dominated by at least two vertices of D …