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On the extremal values for the Mostar index of trees with given degree sequence

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  • Deng, Kecai
  • Li, Shuchao

Abstract

For a given graph G, the Mostar index Mo(G) is the sum of absolute values of the differences between nu(e) and nv(e) over all edges e=uv of G, where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to u than to v and the number of vertices of G lying closer to v than to u. The degree sequence of a tree is the sequence of the degrees (in descending order) of the non-leaf vertices. This paper determines those trees with a given degree sequence which have the greatest Mostar index. Consequently, all extremal trees with the greatest Mostar index are obtained in the sets of all trees of order n with the maximum degree, the number of leaves, the independence number and the matching number, respectively. On the other hand, some properties of trees with a given degree sequence which have the least Mostar index are given. We also determine those trees with exactly n−3 or n−4 leaves when the degree sequence is given, which have the least Mostar index. At last some numerical results are discussed, in which we calculate the Mostar indices of two sets of molecular graphs: octane isomers and benzenoid hydrocarbons; We compare their Mostar indices with some other distance-based topological indices through their correlations with the chemical properties. The linear model for the Mostar index is better than or as good as the models corresponding to the other distance-based indices.

Suggested Citation

  • Deng, Kecai & Li, Shuchao, 2021. "On the extremal values for the Mostar index of trees with given degree sequence," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305531
    DOI: 10.1016/j.amc.2020.125598
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    References listed on IDEAS

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    1. Tepeh, Aleksandra, 2019. "Extremal bicyclic graphs with respect to Mostar index," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 319-324.
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    Cited by:

    1. Li, Shuchao & Liu, Xin & Sun, Wanting & Yan, Lixia, 2023. "Extremal trees of a given degree sequence or segment sequence with respect to average Steiner 3-eccentricity," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Buyantogtokh, Lkhagva & Azjargal, Enkhbayar & Horoldagva, Batmend & Dorjsembe, Shiikhar & Adiyanyam, Damchaa, 2021. "On the maximum size of stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Liu, Guorong & Deng, Kecai, 2023. "The maximum Mostar indices of unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 439(C).

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