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k-Perfect geodominating sets in graphs

Mojdeh D. A., Rad N. J.

Opuscula Mathematica

2007

Vol. 27, no. 1

51-57

A perfect geodominating set in a graph G is a geodominating set S such that any vertex v ∈ V(G)\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 ∈ V(G)\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.