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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 ...
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 ...
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 ...
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 ...