k-Perfect geodomination is affected by adding a pendant vertex
Doost Ali Mojdeh, Nader Jafari Rad · International Mathematical Forum · 2007
A k−geodominating set is a geodominating set S such that any vertex v ∈ V (G) \\ S is geodominated by a pair x, y of vertices of S with d(x, y) =k. 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 the vertices of S with d(x, y) =k. The cardinality of a minimum perfect geodominating set in G is its perfect geodomination number gp(G) and the cardinality of a minimum k-perfect geodominating set in G is its k-perfect geodomination number gkp(G). We investigate the affection of k-perfect geodomination numbers of a graph G when a pendant vertex is added.