International Journal For Multidisciplinary Research

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Disjoint Perfect Secure Domination in the Cartesian Product and Lexicographic Product of Graphs

Author(s) Renelyn B. Udtohan, Enrico L. Enriquez, Grace M. Estrada, Marie Cris A. Bulay-og, Edward M. Kiunisala
Country Philippines
Abstract Let G be a graph. A dominating set D⊆V(G) is called a secure dominating set of G if for each vertex u∈V(G)∖D, there exists a vertex v∈D such that uv∈ E(G) and the set (D∖{v})∪{u} is a dominating set of G. If every u∈V(G)∖D is adjacent to exactly one vertex in D, then D is a perfect secure dominating set of G. Let D be a minimum perfect secure dominating set of G. If S⊆V(G)∖D is a perfect secure dominating set of G, then S is called an inverse perfect secure dominating set of G with respect to D. A disjoint perfect secure dominating set of G is the set C=D∪S⊆V(G). Furthermore, the disjoint perfect secure domination number, denoted by γ_ps γ_ps (G), is the minimum cardinality of a disjoint perfect secure dominating set of G. A disjoint perfect secure dominating set of cardinality γ_ps γ_ps (G) is called γ_ps γ_ps-set. In this paper, we extended the study on the concept of disjoint perfect secure domination in graphs. Furthermore, we characterized the disjoint perfect secure domination in the Cartesian product and lexicographic product of two graphs.
Keywords domination, perfect secure, inverse perfect secure, disjoint, set, lexicographic, Cartesian
Field Mathematics
Published In Volume 6, Issue 2, March-April 2024
Published On 2024-04-07
Cite This Disjoint Perfect Secure Domination in the Cartesian Product and Lexicographic Product of Graphs - Renelyn B. Udtohan, 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.v06i02.16564
DOI https://doi.org/10.36948/ijfmr.2024.v06i02.16564
Short DOI https://doi.org/gtqxz5
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