The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains

Document Type : Research Paper

Authors

College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China

Abstract

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as
$J(G)=\frac{m}{\mu+1}\sum\limits_{uv\in E} \frac{1}{\sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=\frac{m}{\mu+1}\sum\limits_{uv\in E} \frac{1}{\sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=\sum\limits_{v\in V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the number of edges and $\mu$ is the cyclomatic number of $G$. They are useful distance-based descriptor in chemometrics. In this paper, we focus on the extremal graphs of spiro and polyphenyl hexagonal chains with respect to the Balaban index and the sum-Balaban index.

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References

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Iranian Journal of Mathematical Chemistry
Volume 9, Issue 4
December 2018
Pages 241-254

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