M-Polynomial and Degree-Based Topological Indices
By Emeric Deutsch, Sandi Klavvzar. 2014
287 citations recorded by the source corpus.
Let $G$ be a graph and let $m_{ij}(G)$, $i,j\ge 1$, be the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. The {\em $M$-polynomial} of $G$ is introduced with $\displaystyle{M(G;x,y) = \sum_{i\le j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $M$-polynomial. The new approach is also illustrated with examples.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9b4cd427191dbea9fc8b2522d3c24e84bc632664
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In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Forgotten Polynomial and Forgotten Index of Certain Interconnection Networks (2017, background): “Topological indices [13, 14, 15, 16, 17, 18, 19, 20, 21, 22] gives a good predictions of variety of physico-chemical properties of chemical compounds containing boiling point, heat of evaporation, heat of formation, chromatographic retention times, surface tension, vapor pressure etc.”