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.
- 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.
