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

Opuscula Mathematica

# k-perfect geodominating sets in graphs

Doost Ali Mojdeh

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
• University of Mazandaran, Department of Mathematics Babolsar, Iran, P.O. Box 47416-1467