Rainbow numbers for certain graphs

A subgraph of an edge-coloured graph is rainbow if all of its edges have different colours. For a given a graph H, a rainbow number is the minimum number r b ( n , H ) such that any edge-colouring of K n with at least r b ( n , H ) number of colours contains a rainbow copy of H. We determine the rainbow numbers for certain stars with one edge added and for complete graphs with one edge added.