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Extremal catacondensed benzenoids with respect to the Mostar index

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Abstract

For a given graph G, the Mostar index \(Mo(G)\) is the sum of absolute values of the differences between \(n_u(e)\) and \(n_v(e)\) over all edges \(e = uv\) of G, where \(n_u(e)\) and \(n_v(e)\) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. In this paper, the tree-type hexagonal systems (catacondensed hydrocarbons) with the least and the second least Mostar indices are determined. We also show some properties of tree-type hexagonal systems with the greatest Mostar index. And as a by-product, we determine the graph with the greatest Mostar index among tree-type hexagonal systems with exactly one full-hexagon. These results generalize some known results on extremal hexagonal chains.

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Acknowledgements

The authors would like to express their sincere gratitude to all of the referees for their insightful comments and suggestions, which led to a number of improvements to this article.

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362000, Fujian, People’s Republic of China

    Kecai Deng

  2. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Shuchao Li

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  1. Kecai Deng
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  2. Shuchao Li
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Correspondence to Shuchao Li.

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Kecai Deng is partially supported by NSFC (No.11701195) and by Scientific Research Funds of Huaqiao University (No.16BS808) and Shuchao Li is partially ssupported by NSFC (Nos. 11671164, 11271149).

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Deng, K., Li, S. Extremal catacondensed benzenoids with respect to the Mostar index. J Math Chem 58, 1437–1465 (2020). https://doi.org/10.1007/s10910-020-01135-0

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  • DOI: https://doi.org/10.1007/s10910-020-01135-0

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