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

Opuscula Mathematica

Strong geodomination in graphs

Nader Jafari Rad
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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  • Nader Jafari Rad
  • 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
  • Received: 2007-04-24.
  • Revised: 2007-11-18.
  • Accepted: 2007-12-04.
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Cite this article as:
Nader Jafari Rad, Doost Ali Mojdeh, Strong geodomination in graphs, Opuscula Math. 28, no. 3 (2008), 279-285

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