Outer-restrained Domination in the Lexicographic Product of Two Graphs

Author(s)	Celart A. Tuble, Enrico L. Enriquez, Katrina B. Fuentes, Grace M. Estrada, Edward M. Kiunisala
Country	Philippines
Abstract	Let G be a connected simple graph. A set S⊆V(G) is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in (G)∖S . A set S of vertices of a graph G is an outer-restrained dominating set if every vertex not in S is adjacent to some vertex in S and V(G)∖S is a restrained set. The outer-restrained domination number of G, denoted by (γ_r ) ̃(G) is the minimum cardinality of an outer-restrained dominating set of G. An outer-restrained set of cardinality (γ_r ) ̃(G) will be called a (γ_r ) ̃(G) -set. This study is an extension of an existing research on outer-restrained domination in graphs. In this paper, we characterized the outer-restrained domination in graphs under the lexicographic product of two graphs.
Keywords	dominating, restrained, outer-connected, outer-restrained, lexicographic
Field	Mathematics
Published In	Volume 6, Issue 2, March-April 2024
Published On	2024-04-14
DOI	https://doi.org/10.36948/ijfmr.2024.v06i02.17204

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