Inverse Fair Restrained Domination in the Corona of Two 
Graphs

Villa S. Verdad; Enrico L. Enriquez

doi:https://doi.org/10.14445/22315373/IJMTT-V69I12P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 12 | Year 2023 | Article Id. IJMTT-V69I12P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I12P504

Inverse Fair Restrained Domination in the Corona of Two Graphs

Villa S. Verdad, Enrico L. Enriquez

Received	Revised	Accepted	Published
22 Oct 2023	30 Nov 2023	11 Dec 2023	30 Dec 2023

Abstract

Let 𝐺 be a connected simple graph. A dominating subset S of 𝑉(𝐺) is a fair dominating set in 𝐺 if all the vertices not in 𝑆 are dominated by the same number of vertices from 𝑆. A fair dominating set 𝑆 ⊆ 𝑉(𝐺) is a fair restrained dominating set if every vertex not in 𝑆 is adjacent to a vertex in 𝑆 and to a vertex in 𝑉(𝐺) ∖ 𝑆. Alternately, a fair dominating set 𝑆 ⊆ 𝑉(𝐺) is a fair restrained dominating set if 𝑁[𝑆] = 𝑉(𝐺) and 〈𝑉(𝐺) ∖ 𝑆〉 is a subgraph without isolated vertices. Let 𝐷 be a minimum fair restrained dominating set of 𝐺. A fair restrained dominating set 𝑆 ⊆ (𝑉(𝐺) ∖ 𝐷) is called an inverse fair restrained dominating set of G with respect to 𝐷. The inverse fair restrained domination number of 𝐺 denoted by 𝛾𝑓𝑟𝑑 −1 (𝐺) is the minimum cardinality of an inverse fair restrained dominating set of 𝐺. An inverse fair restrained dominating set of cardinality 𝛾𝑓𝑟𝑑 −1 (𝐺) is called 𝛾𝑓𝑟𝑑 −1 (𝐺)-set. In this paper, the researchers investigate the concept and give some important results on inverse fair restrained dominating sets under the corona of two graphs.

Keywords

Dominating set, Fair dominating set, Fair restrained dominating set, Inverse fair restrained dominating set, Corona of two graphs.

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Citation :

Villa S. Verdad, Enrico L. Enriquez, "Inverse Fair Restrained Domination in the Corona of Two Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 12, pp. 27-35, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I12P504