International Journal of Mathematics Trends and Technology
Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P517
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 secure dominating set if for each u ∈ V(G) \ S there exists v ∈ S such that u is adjacent to v and (S {v}) ∪ {u} is a dominating set. A secure dominating set S is called a perfect secure dominating set of G if each u ∈ V(G) \ S is dominating by exactly one element of S. Further, if D is a minimum perfect secure dominating set of G, then a perfect secure dominating set S ⊆ V(G) \ D is called an inverse perfect secure dominating set of G with respect to D. In this paper, we investigate the concept and give some important results.
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Cristina S. Castañares, Enrico L. Enriquez, "Inverse Perfect Secure Domination in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 150-156, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P517
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