Opuscula Math. 28, no. 3 (2008), 279-285

Opuscula Mathematica

# Strong geodomination in graphs

Doost Ali Mojdeh

Abstract. A pair $$x$$, $$y$$ of vertices in a nontrivial connected graph $$G$$ is said to geodominate a vertex $$v$$ of $$G$$ if either $$v \in \{x, y\}$$ or $$v$$ lies in an $$x - y$$ geodesic of $$G$$. A set $$S$$ of vertices of $$G$$ is a geodominating set if every vertex of $$G$$ is geodominated by some pair of vertices of $$S$$. In this paper we study strong geodomination in a graph $$G$$.

Keywords: geodomination, $$k$$-geodomination, open geodomination.

Mathematics Subject Classification: 05C12, 05C70.

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• Shahrood University of Technology, Department of Mathematics, Shahrood, Iran
• Doost Ali Mojdeh
• University of Mazandaran, Department of Mathematics, Babolsar, Iran, P.O. Box 47416-1467
• Institute for Studies in Theoretical Physics and Mathematics, (IPM), Tehran, Iran
• Revised: 2007-11-18.
• Accepted: 2007-12-04.