investigate the nonnegative signed dom- ination number NN s with emphasis on regular, triangle-free graphs and trees. We give lower and upper bounds on NN s for regular graphs and prove that n=3 is the best possible upper bound on this parameter for a cubic graph of order n. investigate the nonnegative signed dom- ination number NNs with emphasis on regular, triangle-free graphs and trees. We give lower and upper bounds on NNs for regular graphs and prove that n=3 is the best possible upper bound on this parameter for a cubic graph of order n. Also, we bound NNs (T) for a tree T from above and below and characterize all trees attaining the bounds.
