Opuscula Math. 27, no. 1 (2007), 51-57

 
Opuscula Mathematica

k-perfect geodominating sets in graphs

Doost Ali Mojdeh
Nader Jafari Rad

Abstract. A perfect geodominating set in a graph \(G\) is a geodominating set \(S\) such that any vertex \(v \in V(G)\setminus S\) is geodominated by exactly one pair of vertices of \(S\). A \(k\)-perfect geodominating set is a geodominating set \(S\) such that any vertex \(v \in V(G)\setminus S\) is geodominated by exactly one pair \(x\), \(y\) of vertices of \(S\) with \(d(x,y)=k\). We study perfect and \(k\)-perfect geodomination numbers of a graph \(G\).

Keywords: geodominating set, perfect geodomination number, pendant vertex, pendant edge.

Mathematics Subject Classification: 05C69.

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  • Doost Ali Mojdeh
  • University of Mazandaran, Department of Mathematics Babolsar, Iran, P.O. Box 47416-1467
  • Nader Jafari Rad
  • University of Mazandaran, Department of Mathematics Babolsar, Iran, P.O. Box 47416-1467
  • Received: 2005-12-12.
Opuscula Mathematica - cover

Cite this article as:
Doost Ali Mojdeh, Nader Jafari Rad, k-perfect geodominating sets in graphs, Opuscula Math. 27, no. 1 (2007), 51-57

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