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Extremal phenylene chains with respect to detour indices

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Abstract

Computing topological indices of molecular structures is a fundamental and classical topic. In organic chemistry, hexagonal and quadrilateral molecular structures are very common. The detour index \(\omega (G)\) of a connected graph G is defined as \(\omega (G)=\sum \nolimits _{\{u,v\}\subseteq V(G)}l_{G}(u,v)\), where \(l_{G}(u,v)\) denotes the detour distance between vertices u and v. In this study, we obtain the explicit analytical expression for detour index of phenylene chains with a fixed number of hexagons. Further minimal and maximal phenylene chains are obtained.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Hechao Liu & Xiaona Fang

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  1. Hechao Liu
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  2. Xiaona Fang
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Correspondence to Hechao Liu.

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Research supported by the National Natural Science Foundation of China (through Grant No. 11971180, 11571123), the Guangdong Provincial Natural Science Foundation of China (through Grant No. 2019A1515012052).

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Liu, H., Fang, X. Extremal phenylene chains with respect to detour indices. J. Appl. Math. Comput. 67, 301–316 (2021). https://doi.org/10.1007/s12190-020-01483-9

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  • DOI: https://doi.org/10.1007/s12190-020-01483-9

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