Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285220201201Outer-weakly convex domination number of graphs2072151406610.22049/cco.2020.26871.1154ENJonecis ADayapUniversity of San Jose-Recoletos0000-0003-1047-1490RichardAlcantaraUniversity of CebuRomaAnoosCebu Technological University-San Fernando ExtensionJournal Article20200515For a given simple graph $G=(V,E)$, a set $Ssubseteq V$ is an outer-weakly convex dominating set if every vertex in $Vsetminus S$ is adjacent to some vertex in $S$ and $Vsetminus S$ 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. http://comb-opt.azaruniv.ac.ir/article_14066_322f3d041cb8dc320b968fd5222905f9.pdf