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A formula with its applications on the difference of Zagreb indices of graphs

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Abstract

In this note we focus on the difference \(ZD_1(G)=M_1(G)-M_2(G)\) of chemical graphs G where \(M_1(G)\) and \(M_2(G)\) are first and second Zagreb indices of G, respectively. An explicit formula is obtained for computing the value of \(ZD_1\) of chemical trees with maximum degree 3. As the applications of this formula, we get some results on the properties of \(ZD_1\) of chemical graphs, in particular, we solve the inverse problem for \(ZD_1\) by showing that there is a chemical tree T with \(ZD_1(T)=t\) for any integer \(t\in (-\infty ,2]\).

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Acknowledgements

The authors are much grateful to two anonymous referees for their careful reading and helpful comments on our paper.

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Authors and Affiliations

  1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, Jiangsu, People’s Republic of China

    Kexiang Xu & Fang Gao

  2. School of Mathematics and Computer Science, Chizhou University, Chizhou, 247000, Anhui, People’s Republic of China

    Fang Gao

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Republic of Korea

    Kinkar Chandra Das

  4. The Ruđer Bošković Institute, 10002, Zagreb, Croatia

    Nenad Trinajstić

Authors
  1. Kexiang Xu
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  2. Fang Gao
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  3. Kinkar Chandra Das
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  4. Nenad Trinajstić
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Correspondence to Kinkar Chandra Das.

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The first author is supported by NNSF of China (No. 11671202). The third author is supported by the Sungkyun research fund, Sungkyunkwan University, 2017.

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Xu, K., Gao, F., Das, K.C. et al. A formula with its applications on the difference of Zagreb indices of graphs. J Math Chem 57, 1618–1626 (2019). https://doi.org/10.1007/s10910-019-01025-0

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  • DOI: https://doi.org/10.1007/s10910-019-01025-0

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