Solvable Lie algebras with $N(R_n,m,r)$ nilradical

In this paper‎, ‎we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical‎, ‎by using the derivation algebra and the automorphism group of $N(R_n,m,r)$‎. ‎We also prove that these solvable Lie algebras are complete and unique‎, ‎up to isomorphism‎.