Abstract: A double dominating set D in a connected nontrivial graph G without isolated vertices is a 1-movable double dominating set of G if for every either is a double dominating set, or there exists a vertex such that is a double dominating set of G. The minimum cardinality of a 1-movable double dominating set of G, denoted by is the 1-movable double domination number of G. A 1-movable double dominating set with cardinality is called a -set of G. In this paper, we characterize those graphs G which possess a 1-movable double dominating set. We also characterize the 1-movable double dominating sets in the join and corona of graphs and determine the corresponding 1-movable double domination numbers of these graphs.
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Keywords and phrases: double domination, 1-movable double domination, strictly 1-movable domination, external and internal private neighbors, join, corona.
Received: December 28, 2022; Accepted: February 18, 2023; Published: April 11, 2023
How to cite this article: Jocecar Lomarda-Hinampas and Sergio R. Canoy, Jr., 1-movable double domination in some binary operations of graphs, Advances and Applications in Discrete Mathematics 38(2) (2023), 159-178. http://dx.doi.org/10.17654/0974165823026
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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