We study the maximum value of the difference between the metric dimension and the
determining number of a graph as a function of its order. We develop a technique that uses …

A locating-dominating set of an undirected graph is a subset of vertices S such that S is
dominating and for every u, v∉ S, the neighbourhood of u and v on S are distinct (ie N (u)∩ …

Let G be a graph and let k and j be positive integers. A subset D of the vertex set of G is a k-
dominating set if every vertex not in D has at least k neighbors in D. The k-domination …

The annihilation number $ a $ of a graph is an upper bound of the independence number
$\alpha $ of a graph. In this article we characterize graphs with equal independence and …

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 …

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. The 2-domination number γ 2 (G) is the minimum cardinality of a …

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 set $ S $ of vertices in a graph $ G $ is a dominating set if every‎‎ vertex of $ VS $ is
adjacent to some vertex in $ S $‎.‎ The domination‎‎ number $\gamma (G) $ is the minimum …

In this note, we present the two inequalities γk≤ n− αj (Hm) and γk≤ n+ γk− 1+ nk− 1 2,
where γk is the k-domination number, n is the order, αj (Hm) is the j-independence number …

Abstract In 2014, Desormeaux et al.(Discrete Math 319: 15–23, 2014) proved a relationship
between the annihilation number and 2-domination number of a tree. In this note, we …