A note on generalized rainbow connection of connected graphs and their number of EDGES

In the paper "A note on generalized rainbow connection of connected graphs and their number of EDGES", we first focus to improve the upper bound of the (1, l)-rainbow connection number depending on the size of connected graphs. Using this result, we characterize all connected graphs having the large (1, 2)-rainbow connection number. Moreover, we also determine the (1, l)-rainbow connection number in a connected graph G containing a sequence of cut-edges.