VDB-Hosoya Index of Hexagonal Chains

Document Type : Research Paper

Authors

Instituto de Matem\'{a}ticas‎, ‎Universidad de Antioquia‎, ‎Medell\'{\i}n‎, ‎Colombia

10.22052/ijmc.2025.257234.2036

Abstract

‎Our main interest in this paper is the study of the Hosoya index $Z\left(G;\varphi \right) $ of weighted graphs $\left( G;\varphi \right) $‎, ‎when $G$ is a hexagonal chain with weight function induced by a vertex-degree-based topological index $\varphi$‎. ‎Recall that a hexagonal chain is a special type of hexagonal systems‎, ‎natural graph representations of benzenoid hydrocarbons‎. ‎On the other hand‎, ‎vertex-degree based topological indices are (molecular) graph descriptors which play a significant role in chemical graph theory‎.
‎Concretely‎, ‎if $G$ is a hexagonal chain and $\varphi$ is a vertex-degree-based topological index‎, ‎we give a method to compute $Z\left(G;\varphi \right) $ in terms of products of namely four types of $4\times 4$ matrices associated to $\varphi$‎. ‎As a consequence‎, ‎under certain conditions on $\varphi$‎, ‎we show that the $\varphi$-weighted linear hexagonal chain attains the minimal value of the Hosoya index‎, ‎among all $\varphi$-weighted hexagonal chains‎.

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References

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Iranian Journal of Mathematical Chemistry
Volume 16, Issue 4
In Progress
December 2025
Pages 337-353

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