on the m-polynomial of planar chemical graphs

Let $g$ be a graph and let $m_{i,j}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the $m$polynomial of $g$ is $m(g;x,y) = sum_{ile j} m_{i,j}(g)x^iy^j$. with $m(g;x,y)$ in hands, numerous degreebased topological indices of $g$ can be routinely computed. in this note a formula for the $m$polynomial of planar (chemical) graphs which have only vertices of degrees $2$ and $3$ is given that involves only invariants related to the degree $2$ vertices and the number of faces. the approach is applied on several families of chemical graphs. in one of these families an error from the literature is corrected.