On the M-polynomial of planar chemical graphs

Document Type: Research Paper

Authors

1 Polytechnic Institute of New York University (retired)

2 Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

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

Main Subjects


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