Opuscula Mathematica

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

k-perfect geodominating sets in graphs



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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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