Outer-weakly convex domination number of graphs

Document Type : Original paper

Authors

1 University of San Jose-Recoletos

2 University of Cebu

3 Cebu Technological University-San Fernando Extension

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. 

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References

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Communications in Combinatorics and Optimization
Volume 5, Issue 2
December 2020
Pages 207-215

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