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.