Outer-Connected Inverse Domination in Graphs

Author(s)	Ami Rose E. Montebon, Enrico L. Enriquez, Grace M. Estrada, Mark Kenneth C. Engcot, Margie L. Baterna
Country	Philippines
Abstract	Let be a connected simple graph. A subset of is a dominating set of if for every , there exists such that. A set is said to be an outer-connected dominating set in if is dominating and either or is connected. Let be a minimum dominating set of . A nonempty subset is an outer-connected inverse dominating set of , if is an inverse dominating set with respect to and the subgraph induced by is connected. The outer-connected inverse domination number of , is denoted by , that is, the minimum cardinality of an outer-connected inverse dominating set of . In this paper, we initiate the study of the concept and give the outer-connected inverse domination number of some special graphs. Further, we give the characterization of the outer-connected inverse dominating set in the join of two nontrivial connected graphs.
Keywords	dominating set, outer-connected dominating set, inverse dominating set, outer-connected inverse dominating set
Field	Mathematics
Published In	Volume 6, Issue 6, November-December 2024
Published On	2024-12-25
DOI	https://doi.org/10.36948/ijfmr.2024.v06i06.33788
Short DOI	https://doi.org/g8w2wb

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