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Domination parameters with number 2: Interrelations and algorithmic consequences
(Elsevier Science, 2018-01)
In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied ...
Improved algorithms for k-domination and total k-domination in proper interval graphs
(Springer, 2018-07)
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 ...
New algorithms for weighted k-domination and total k-domination problems in proper interval graphs
(Elsevier Science, 2019-11)
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 is a set of vertices such that every ...
The Identifying Code, the Locating-dominating, the Open Locating-dominating and the Locating Total-dominating Problems Under Some Graph Operations
(Elsevier, 2019)
The problems of determining minimum identifying, locating-dominating, open locating-dominating or locating total-dominating codes in a graph G are variations of the classical minimum dominating set problem in G and are all ...
Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
(Elsevier Science, 2018-10)
We consider two variations of graph total domination, namely, k-tuple total domination and total {k}-domination (for a fixed positive integer k). Their related decision problems are both NP-complete even for bipartite ...
Facets of the polytope of legal sequences
(Elsevier, 2017-11)
A sequence of vertices in a graph is called a (total) legal dominating sequence if every vertex in the sequence (totally) dominates at least one vertex not dominated by the ones that precedes it, and at the end all vertices ...
Grundy domination and zero forcing in Kneser graphs
(Open Journal Systems, 2019-06)
In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers ...
Total dominating sequences in trees, split graphs, and under modular decomposition
(Elsevier Science, 2018-05)
A sequence of vertices in a graph G with no isolated vertices is called a total dominating sequence if every vertex in the sequence totally dominates at least one vertex that was not totally dominated by preceding vertices ...
An integer programming approach for solving a generalized version of the Grundy domination number
(Elsevier Science, 2021-10-15)
A legal dominating sequence of a graph is an ordered dominating set of vertices where each element dominates at least another one not dominated by its predecessors in the sequence. The length of a largest legal dominating ...
Brazilian credit union member groups: borrower-dominated, saver-dominated or neutral behavior?
(BAR - Brazilian Administration Review, 2019)