Solvable Leibniz algebras with NF n ⊕ [...] F m 1 nilradical
All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.