Secure Super Domination in Graphs

Hemeh Luck M. Maravillas; Enrico L. Enriquez

doi:https://doi.org/10.14445/22315373/IJMTT-V67I8P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P504

Secure Super Domination in Graphs

Hemeh Luck M. Maravillas, Enrico L. Enriquez

Abstract

Let 𝐺 = (𝑉(𝐺),𝐸(𝐺)) be a connected simple graph. A subset 𝑆 of 𝑉(𝐺) is a dominating set of 𝐺 if for every 𝑢 ∈ 𝑉(𝐺)\𝑆, there exists 𝑣 ∈ 𝑆 such that 𝑢𝑣 ∈ 𝐸(𝐺). A dominating set 𝑆 is called a super dominating set if for very vertex 𝑢 ∈ 𝑉(𝐺)\𝑆, there exists 𝑣 ∈ 𝑆 such that 𝑁𝐺 (𝑣) ∩ (𝑉(𝐺)\𝑆) = {𝑢}. A super dominating set 𝑆 is called a secure super dominating set if for every vertex 𝑢 ∈ 𝑉(𝐺)\𝑆, there exists 𝑣 ∈ 𝑆 such that (𝑆\{𝑣}) ∪ {𝑢} is a super dominating set of 𝐺. In this paper, we investigate the concept and give some important results.

Keywords

dominating set, super dominating set, secure dominating set, secure super dominating set

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Citation :

Hemeh Luck M. Maravillas, Enrico L. Enriquez, "Secure Super Domination in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 38-44, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P504