Let G be a connected graph. Then a non-empty  is a 2-movable dominating set of G if S is a dominating set and for every pair   is a dominating set in G, or there exist  such that u and v are adjacent to x and y, respectively, and  is a dominating set in G. The 2-movable domination number of G, denoted by  is the minimum cardinality of a 2-movable dominating set of G. A 2-movable dominating set with cardinality equal to  is called -set of G.

This paper obtains 2-movable domination numbers for the corona and join of graphs.

domination, 2-movable domination, corona, join.

Received: January 23, 2024; Revised: September 28, 2024; Accepted: November 20, 2024; Published: November 28, 2024

How to cite this article: Ariel C. Pedrano and Rolando N. Paluga, On 2-movable domination in the join and corona of graphs, Advances and Applications in Discrete Mathematics 42(2) (2025), 89-96. https://doi.org/10.17654/0974165825007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] J. Blair, R. Gera and S. Horton, Movable dominating sensor sets in networks, J. Combin. Math. Combin. Comput. 77 (2011), 103-123.
[2] O. Ore, Theory of Graphs, American Mathematical Society Colloquium Publications, Vol. XXXVIII, 1962.