Abstract
The Merrifield-Simmons index (\(\sigma \)) is an important molecular descriptor in chemical graph theory. Merrifield-Simmons index is defined as the total number of independent sets of the graph. The first Zagreb index (\(M_{1}\)), second Zagreb index (\(M_{2}\)), forgotten index (F) are another three important molecular descriptors in chemical graph theory, which often used to study molecular complexity, chirality, and other chemical properties. In this paper, we study the relationship between the Merrifield-Simmons index \(\sigma \) and \(M_{1}\) (resp. \(M_{2}\), F). We determine some sharp bounds on the difference between \(\sigma \) and \(M_{1}\) (resp. \(M_{2}\), F) for (connected) graphs, self-centered graphs, graphs with given independence number. We also compare \(\sigma \) with \(M_{1}\) (resp. \(M_{2}\), F) for (molecular) graphs, (molecular) trees, hexagonal chains, bipartite graphs, k-power graphs, graphs with given the number of cut vertices.
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Acknowledgements
This research is partially supported by the National Natural Science Foundation of China (Grant No. 11971180), the Guangdong Provincial Natural Science Foundation (Grant No. 2019A1515012052), the Characteristic Innovation Project of General Colleges and Universities in Guangdong Province (Grant No. 2022KTSCX225) and the Guangdong Education and Scientific Research Project (Grant No. 2021GXJK159).
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Liu, H. Comparison between Merrifield-Simmons index and some vertex-degree-based topological indices. Comp. Appl. Math. 42, 89 (2023). https://doi.org/10.1007/s40314-023-02240-x
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DOI: https://doi.org/10.1007/s40314-023-02240-x