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Secure Inverse Domination in the Corona and Lexicographic Product of Two Graphs

Author(s) Jesica P. Dagodog, Enrico L. Enriquez, Grace M. Estrada, Marie Cris A. Bulay-og, Edward M. Kiunisala
Country Philippines
Abstract As secure domination and inverse domination garnered attention from various researchers, the combination of the two also raised a certain amount of curiosity. This paper aimed to investigate the secure inverse domination in graphs which is defined as follows. Let G be a connected simple graph and let D be a minimum dominating set of G. A dominating set S⊆V(G)∖D is an inverse dominating set of G with respect to D. The set S is called a secure inverse dominating set of G if for every u∈V(G)∖S, there exists v∈S such that uv∈E(G) and the set (S∖{v})∪{u} is a dominating set of G. The secure inverse domination number of G, denoted by γ_s^((-1) ) (G), is the minimum cardinality of a secure inverse dominating set of G. A secure inverse dominating set of cardinality γ_s^((-1) ) (G) is called γ_s^((-1) )-set. Particularly, the researchers examined and provided the characterization of secure inverse dominating set in the corona and lexicographic product of two graphs in this study. Moreover, the secure inverse domination number of graphs under the binary operations corona and lexicographic product were determined.
Keywords Dominating Sets, Corona of Two Graphs, Inverse Dominating Sets, Secure Dominating Sets, Lexicographic Product of Two Graphs
Field Mathematics
Published In Volume 6, Issue 2, March-April 2024
Published On 2024-04-15
Cite This Secure Inverse Domination in the Corona and Lexicographic Product of Two Graphs - Jesica P. Dagodog, Enrico L. Enriquez, Grace M. Estrada, Marie Cris A. Bulay-og, Edward M. Kiunisala - IJFMR Volume 6, Issue 2, March-April 2024. DOI 10.36948/ijfmr.2024.v06i02.16776
DOI https://doi.org/10.36948/ijfmr.2024.v06i02.16776
Short DOI https://doi.org/gtq3d5
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