%0 Journal Article
%T On the M-polynomial of planar chemical graphs
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Deutsch, Emeric
%A Klavžar, Sandi
%D 2020
%\ 07/30/2020
%V 11
%N 2
%P 65-71
%! On the M-polynomial of planar chemical graphs
%K Graph polynomial
%K Degree-based topological index
%K planar graph
%R 10.22052/ijmc.2020.224280.1492
%X 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 degree-based 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.
%U https://ijmc.kashanu.ac.ir/article_106057_81375683c320f653c28092d0868d56fb.pdf