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