International Journal For Multidisciplinary Research
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Volume 6 Issue 5
September-October 2024
Indexing Partners
Identifying Secure Domination in the Cartesian and Lexicographic Products of Graphs
Author(s) | Haridel Aquiles, Marie Cris A. Bulay-og, Grace M. Estrada, Carmelita M. Loquias, Enrico L. Enriquez |
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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 the Cartesian product and lexicographic product of two connected graphs. |
Keywords | domination, secure, identifying, Cartesian, lexicographic |
Field | Mathematics > Logic |
Published In | Volume 6, Issue 2, March-April 2024 |
Published On | 2024-03-08 |
Cite This | Identifying Secure Domination in the Cartesian and Lexicographic Products of Graphs - Haridel Aquiles, Marie Cris A. Bulay-og, Grace M. Estrada, Carmelita M. Loquias, Enrico L. Enriquez - IJFMR Volume 6, Issue 2, March-April 2024. DOI 10.36948/ijfmr.2024.v06i02.14303 |
DOI | https://doi.org/10.36948/ijfmr.2024.v06i02.14303 |
Short DOI | https://doi.org/gtmbkd |
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E-ISSN 2582-2160
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IJFMR DOI prefix is
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