@article {
author = {Deutsch, Emeric and Klavžar, Sandi},
title = {On the M-polynomial of planar chemical graphs},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {11},
number = {2},
pages = {65-71},
year = {2020},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2020.224280.1492},
abstract = {Let $G$ be a graph and let $m_{i,j}(G)$, $i,j\ge 1$, be the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. The $M$-polynomial of $G$ is $M(G;x,y) = \sum_{i\le j} m_{i,j}(G)x^iy^j$. 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.},
keywords = {Graph polynomial,Degree-based topological index,planar graph},
url = {https://ijmc.kashanu.ac.ir/article_106057.html},
eprint = {https://ijmc.kashanu.ac.ir/article_106057_81375683c320f653c28092d0868d56fb.pdf}
}