Let  be a connected graph. A restrained weakly connected 2-dominating set in G is a set D of vertices in G such that every vertex in  is dominated by at least two vertices in D and is adjacent to at least one vertex in  and that the subgraph  weakly induced by D is connected. The restrained weakly connected 2-domination number of G, denoted by  is the smallest cardinality of a restrained weakly connected 2-dominating set in G. In this paper, we study this new parameter and obtain some general results. Furthermore, we also generate closed formulas for the restrained weakly connected 2-domination numbers of some families of graphs.

weakly connected domination, 2-domination, restrained weakly connected 2-domination.

Received: April 7, 2022; Accepted: May 19, 2022; Published: June 1, 2022

How to cite this article: Mae P. Militante and Rolito G. Eballe, Restrained weakly connected 2-domination in graphs, Advances and Applications in Discrete Mathematics 32 (2022), 13-24. http://dx.doi.org/10.17654/0974165822029

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