For a simple graph $G$, assume that $J(G)$ is the vertex cover ideal of $G$ and $J(G)^{(s)}$ is the $s$-th symbolic power of $J(G)$. We prove that $(J(C)^{(s)})=(J(C)^s)$ for all $s\geq 1$ and for all odd cycle $C$. For a simplicial complex $Δ$, we show that $Δ$ is vertex decomposable if $I_Δ^{\vee}$ is weakly polymatroidal. Let $W=G^π$ be a fully clique-whiskering graph, we prove that $J(W)^s$ is weakly polymatroidal for all $s\geq 1$.