Disjoint Perfect Domination in the Cartesian Product of Two Graphs

Author(s)	Ma. Elizabeth N. Diapo, Grace M. Estrada, Marie Cris A. Bulay-og, Edward M. Kiunisala, Enrico L. Enriquez
Country	Philippines
Abstract	Let G be a connected simple graph. A dominating set S ⊆ V (G) is called a perfect dominating set of G if every u ∈ V (G)\S is dominated by exactly one element of S. Let D be a minimum perfect dominating set of G. A perfect dominating set S ⊂ (V (G) \ D) is called an inverse perfect dominating set of G with respect to D. A disjoint perfect dominating set of G is the set C = D ∪ S ⊆ V (G). Furthermore, the disjoint perfect domination number, denoted by γpγp(G), is the minimum cardinality of a disjoint perfect dominating set of G. A disjoint perfect dominating set of cardinality γpγp(G) is called γpγp-set. In this paper, we give some property of the disjoint perfect dominating set in the Cartesian products of two graphs.
Keywords	dominating, perfect, inverse, disjoint, Cartesian product
Field	Mathematics
Published In	Volume 6, Issue 2, March-April 2024
Published On	2024-04-11
Cite This	Disjoint Perfect Domination in the Cartesian Product of Two Graphs - Ma. Elizabeth N. Diapo, Grace M. Estrada, Marie Cris A. Bulay-og, Edward M. Kiunisala, Enrico L. Enriquez - IJFMR Volume 6, Issue 2, March-April 2024. DOI 10.36948/ijfmr.2024.v06i02.16576
DOI	https://doi.org/10.36948/ijfmr.2024.v06i02.16576
Short DOI	https://doi.org/gtqxzz

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