Inverse Doubly Connected Domination in the Lexicographic Product of Two Graphs

Author(s)	Khaty M. Cruz, Enrico L. Enriquez, Katrina B. Fuentes, Grace M. Estrada, Marie Cris A. Bulay-og
Country	Philippines
Abstract	Let G be a nontrivial connected graph. A dominating set D⊆V(G) is called a doubly connected dominating set of G if both 〈D〉 and 〈V(G)\D〉 are connected. Let D be a minimum connected dominating set of G. If S⊆V(G)\D is a connected dominating set of G, then S is called an inverse doubly connected dominating set of G with respect to D. Furthermore, the inverse doubly connected domination number, denoted by γ_cc^(-1) (G) is the minimum cardinality of an inverse doubly connected dominating set of G. An inverse doubly connected dominating set of cardinalities γ_cc^(-1) (G) is called γ_cc^(-1)-set. In this paper, we characterized the inverse doubly connected domination in the lexicographic product of two graphs and give some important results.
Keywords	dominating, doubly connected, inverse, 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.v06i02.17194

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