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All finite-dimensional solvable Leibniz algebras  L , having  N  =  NF n  ⊕F   m    1$\begin{array}{} F_{m}^{1} \end{array} $    as the nilradical and the dimension of  L  equal to  n + m +3 (the maximal dimension) are described.  NF n   andF   m    1$\begin{array}{} F_{m}^{1} \end{array} $    are the null-filiform and naturally graded filiform Leibniz algebras of dimensions  n  and  m , respectively. Moreover, we show that these algebras are rigid.

Solvable Leibniz algebras with NF n ⊕ F m 1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical