Let K be a field and R = K [x1, . . . , xn] be the polynomial ring in n variables over a field K. Let ∆ be a simplicial complex on n vertices and I = I ∆ be its Stanley-Reisner ideal. In this paper, we show that if I is a matroidal ideal then the following conditions are equivalent: (i) ∆ is sequentially Cohen-Macaulay; (ii) ∆ is shellable; (iii) ∆ is vertex decomposable. Also, if I is a minimally generated by u1, . . . , us such that s ≤ 3 or supp(ui) ∪ supp(uj) = {x1, . . . , xn} for all i = j, then ∆ is vertex decomposable. Furthermore, we prove that if I is a monomial ideal of degree 2 then I is weakly polymatroidal if and only if I has linear quotients if and only if I is vertex splittable.