International Journal For Multidisciplinary Research

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Restrained Inverse Domination in the Lexicographic and Cartesian Products of Two Graphs

Author(s) Wenlin Rose E. Alabastro, Enrico L. Enriquez, Katrina B. Fuentes, Grace M. Estrada, Marie Cris A. Bulay-og, Edward M. Kiunisala
Country Philippines
Abstract Let G be a connected simple graph and D be a minimum dominating set of G. A dominating set S⊆V(G)∖D is called an inverse dominating set of G with respect to D. An inverse dominating set S is called a restrained inverse dominating set of G if every vertex not in S is adjacent to a vertex in S and to a vertex in V(G)∖S. The restrained inverse domination number of G, denoted by, γ_r^((-1) ) (G), is the minimum cardinality of a restrained inverse dominating set of G. A restrained inverse dominating set of cardinality γ_r^((-1) ) (G) is called γ_r^((-1) ) (G) is called γ_r^((-1) )-set. This study is an extension of an existing research on restrained inverse domination in graphs. In this paper, we characterized the restrained inverse domination in graphs under the lexicographic and Cartesian products of two graphs.
Keywords dominating, inverse, restrained, set, lexicographic, Cartesian
Field Mathematics
Published In Volume 6, Issue 2, March-April 2024
Published On 2024-03-28
Cite This Restrained Inverse Domination in the Lexicographic and Cartesian Products of Two Graphs - Wenlin Rose E. Alabastro, Enrico L. Enriquez, Katrina B. Fuentes, Grace M. Estrada, Marie Cris A. Bulay-og, Edward M. Kiunisala - IJFMR Volume 6, Issue 2, March-April 2024. DOI 10.36948/ijfmr.2024.v06i02.15681
DOI https://doi.org/10.36948/ijfmr.2024.v06i02.15681
Short DOI https://doi.org/gtppf5
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