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.
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Deutsch, E., & Klavžar, S. (2020). On the M-polynomial of Planar Chemical Graphs. Iranian Journal of Mathematical Chemistry, 11(2), 65-71. doi: 10.22052/ijmc.2020.224280.1492
MLA
Emeric Deutsch; Sandi Klavžar. "On the M-polynomial of Planar Chemical Graphs", Iranian Journal of Mathematical Chemistry, 11, 2, 2020, 65-71. doi: 10.22052/ijmc.2020.224280.1492
HARVARD
Deutsch, E., Klavžar, S. (2020). 'On the M-polynomial of Planar Chemical Graphs', Iranian Journal of Mathematical Chemistry, 11(2), pp. 65-71. doi: 10.22052/ijmc.2020.224280.1492
VANCOUVER
Deutsch, E., Klavžar, S. On the M-polynomial of Planar Chemical Graphs. Iranian Journal of Mathematical Chemistry, 2020; 11(2): 65-71. doi: 10.22052/ijmc.2020.224280.1492
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