A set  is a 1-movable 2-outer-independent dominating set of G if S is a 2-outer-independent dominating set of G and for every   is a 2-outer-independent dominating set of G or there exists a vertex  such that  is a 2-outer-independent dominating set of G. The 1-movable 2-outer- independent domination number of a graph G, denoted by    is the smallest cardinality of a 1-movable 2-outer-independent dominating set of G. A 1-movable 2-outer-independent dominating  set of G with cardinality equal to  is called -set of G. We characterize 1-movable 2-outer-independent dominating set in a graph and the 1-movable 2-outer-independent domination in some special graphs.

1-movable 2-outer-independent domination, 1-movable domination, 2-outer-independent domination, outer-independent domination, 2-domination.

Received: April 10, 2024; Revised: September 28, 2024; Accepted: October 1, 2024; Published: October 8, 2024

How to cite this article: Vanesa S. Miculob, Renario G. Hinampas, Jr and Jocecar L. Hinampas, 1-movable 2-outer-independent dominating sets in graphs, Advances and Applications in Discrete Mathematics 41(7) (2024), 589-602. https://doi.org/10.17654/0974165824039

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