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AIMS Mathematics

2025, Volume 10, Issue 9: 21240-21253. doi: 10.3934/math.2025948
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Maximizing chemical trees of some vertex-degree-based topological indices with given number of pendant vertices

  • School of Mathematics and Computational Sciences, Huaihua University, Huaihua, Hunan, China
  • Published: 16 September 2025

  • MSC : 05C05, 05C09, 05C92

  • A general VDB topological index of $ G $ is defined as

    $ \mathcal{TI}_f(G) = \sum\limits_{v_iv_j\in E(G)} f(d_i,d_j), $

    where $ f(d_i, d_j) $ is a symmetric function, and $ d_i $ represents the degree of $ v_i\in V(G) $. This paper aims to address the maximum chemical tree problem for general vertex-degree-based topological indices with given number of pendant vertices via a unified method. Sufficient conditions for general VDB topological indices to take their maximum value are presented, and as an application, we show that there are six VDB topological indices, including the reciprocal sum-connectivity index, the Sombor index, and the Euler Sombor index, etc., that satisfy these conditions.

    Citation: Zhenhua Su. Maximizing chemical trees of some vertex-degree-based topological indices with given number of pendant vertices[J]. AIMS Mathematics, 2025, 10(9): 21240-21253. doi: 10.3934/math.2025948

    Related Papers:

  • A general VDB topological index of $ G $ is defined as

    $ \mathcal{TI}_f(G) = \sum\limits_{v_iv_j\in E(G)} f(d_i,d_j), $

    where $ f(d_i, d_j) $ is a symmetric function, and $ d_i $ represents the degree of $ v_i\in V(G) $. This paper aims to address the maximum chemical tree problem for general vertex-degree-based topological indices with given number of pendant vertices via a unified method. Sufficient conditions for general VDB topological indices to take their maximum value are presented, and as an application, we show that there are six VDB topological indices, including the reciprocal sum-connectivity index, the Sombor index, and the Euler Sombor index, etc., that satisfy these conditions.



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