@article {
author = {Dayap, Jonecis and Alcantara, Richard and Anoos, Roma},
title = {Outer-weakly convex domination number of graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {5},
number = {2},
pages = {207-215},
year = {2020},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26871.1154},
abstract = {For a given simple graph $G=(V,E)$, a set $S\subseteq V$ is an outer-weakly convex dominating set if every vertex in $V\setminus S$ is adjacent to some vertex in $S$ and $V\setminus S$ is a weakly convex set. The \emph{outer-weakly convex domination number} of a graph $G$, denoted by $\widetilde{\gamma}_{wcon}(G)$, is the minimum cardinality of an outer-weakly convex dominating set of $G$. In this paper, we initiate the study of outer-weakly convex domination as a new variant of graph domination and we show the close relationship that exists between this novel parameter and other domination parameters of a graph. Furthermore, we obtain general bounds on $\widetilde{\gamma}_{wcon}(G)$ and, for some particular families of graphs, we obtain closed formula. },
keywords = {convex domination,weakly-convex domination,outer-connected domination,outer-convex domination,outer-weakly convex domination},
url = {http://comb-opt.azaruniv.ac.ir/article_14066.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14066_322f3d041cb8dc320b968fd5222905f9.pdf}
}