Identifying Secure Domination in the  Join and Corona of Graphs

Author(s)	Haridel A Aquiles, Enrico L Enriquez
Country	Philippines
Abstract	Let G be a connected simple graph. A subset S of V(G) is a dominating set of G if for every v∈V(G)\S, there exists x∈S such that xv∈E(G). An Identifying code of a graph G is a dominating set C⊆V(G) such that for every v∈V(G),N_G [v]∩C is distinct. An identifying code of a graph G is an identifying secure dominating set if for each u∈V(G)\C, there exists v∈C such that uv∈E(G) and the set (C\{v})∪{u} is a dominating set of G. The minimum cardinality of an identifying secure dominating set of G, denoted by γ_s^ID, is called the identifying secure domination number of G. In this paper, the researchers initiate the study of the concept and give some important results. In particular, the researchers show some properties of the identifying secure dominating sets in join and corona of two graphs.
Keywords	domination, secure, identifying, join, corona
Field	Mathematics > Logic
Published In	Volume 6, Issue 1, January-February 2024
Published On	2024-02-17
Cite This	Identifying Secure Domination in the Join and Corona of Graphs - Haridel A Aquiles, Enrico L Enriquez - IJFMR Volume 6, Issue 1, January-February 2024. DOI 10.36948/ijfmr.2024.v06i01.13366
DOI	https://doi.org/10.36948/ijfmr.2024.v06i01.13366
Short DOI	https://doi.org/gtjt2v

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