The multiplicative Zagreb co-indices on two graph operators

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The first and second multiplicative Zagreb co-indices are defined as:
$$\overline\prod_1(G)=\prod_{uv\notin E(G)}[d_G(u)+d_G(v)],\quad\overline\prod_2(G)=\prod_{uv\notin E(G)}[d_G(u)d_G(v)], $$
respectively, where $d_G(u)$ is the degree of the vertex $u$ of $G$. The aim of this paper is to investigate the multiplicative Zagreb co-indices of the subdivision graphs of tadpole graphs and wheel graphs.