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Inverse Sum Indeg Reciprocal Status Index and Co-index of Graphs

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Abstract

Due to the increasing demand for new materials and drugs in the manufacturing and pharmaceutical fields, it is difficult to meet the requirements of high-throughput screening of materials and drugs by measuring the physical and chemical properties of molecular structures with traditional methods. Researchers seek to reveal the relationship between molecular physical and chemical properties and topological index. In this work, we propose the inverse sum indeg reciprocal status index and inverse sum indeg reciprocal status co-index of a graph G, i.e., \(ISIRS(G) = \sum _{uv\in E(G)} \frac{rs(u)rs(v)}{rs(u)+rs(v)}\) and \({\overline{ISIRS}}(G) = \sum _{uv\notin E(G)} \frac{rs(u)rs(v)}{rs(u)+rs(v)}\), where \(rs(u)=\sum _{v\in V(G)}\frac{1}{d(u,v)}\), and d(u, v) denotes the distance between u and v in G. Afterwards, we establish some sharp bounds for these indices. Furthermore, we determine the inverse sum indeg reciprocal status (co-)index of some standard graphs. Finally, we suggest correlations between inverse sum indeg reciprocal status (co-)index and some properties of octane isomers and boiling points of benzenoid hydrocarbon and show that they can well predict the physical and chemical properties of molecules.

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Some or all data, models, or code generated or used during the study are available from the corresponding author by request.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (Nos. 61977016, 61572010), Natural Science Foundation of Fujian Province (Nos. 2020J01164, 2017J01738).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, Fujian, People’s Republic of China

    Zhengqin Yu, Shuming Zhou & Tao Tian

  2. Center for Applied Mathematics of Fujian Province, Fujian Normal University, Fuzhou, 350117, Fujian, People’s Republic of China

    Shuming Zhou

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  1. Zhengqin Yu
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Correspondence to Shuming Zhou.

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Yu, Z., Zhou, S. & Tian, T. Inverse Sum Indeg Reciprocal Status Index and Co-index of Graphs. Circuits Syst Signal Process 42, 2007–2027 (2023). https://doi.org/10.1007/s00034-022-02229-7

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