A nonempty subset S of V(G) is a 1-movable restrained perfect dominating set of G if S = V(G) or S ⊂ V(G) is a restrained perfect dominating set of G and for every v ∈ S, there exists   such that  is a restrained perfect dominating set of G. The smallest cardinality of a 1-movable restrained perfect dominating set of G is called 1-movable restrained perfect domination number of G, denoted by . A 1-movable restrained perfect dominating set of G of cardinality  is called a -set of G. This paper characterizes 1-movable restrained perfect dominating sets in the join and corona of two connected graphs.

restrained domination, perfect domination, restrained perfect domination, 1-movable domination, 1-movable restrained perfect domination.

Received: December 28, 2022; Accepted: February 21, 2023; Published: March 27, 2023

How to cite this article: Renario G. Hinampas, Jr. and Jocecar L. Hinampas, Some results on 1-movable restrained perfect dominating sets in the join and corona of graphs, Advances and Applications in Discrete Mathematics 38(1) (2023), 101-109. http://dx.doi.org/10.17654/0974165823022

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

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