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Outer-weakly convex domination number of graphs | ||
| Communications in Combinatorics and Optimization | ||
| دوره 5، شماره 2، اسفند 2020، صفحه 207-215 اصل مقاله (361.87 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26871.1154 | ||
| نویسندگان | ||
| Jonecis A Dayap* 1؛ Richard Alcantara2؛ Roma Anoos3 | ||
| 1University of San Jose-Recoletos | ||
| 2University of Cebu | ||
| 3Cebu Technological University-San Fernando Extension | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| convex domination؛ weakly-convex domination؛ outer-connected domination؛ outer-convex domination؛ outer-weakly convex domination | ||
| مراجع | ||
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