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The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices

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  • Zhenhua Su
  • Zikai Tang

Abstract

Topological indices are widely used molecular structure descriptors in chemistry and pharmaceutics, which help analyze and predict the physicochemical properties and biological activity of compounds. Focusing on the discriminative power, researchers introduced the general exponential VDB topological index, which is defined as follows: TefG=∑uv∈EGefdu,dv. Our current work focuses on studying of some exponential VDB topological indices using general methods. In the paper, we characterize the sufficient conditions for that (1) the graph Mn,k is the minimal TefG among unicyclic graph with girth k and (2) the graph Hn,k is the maximal TefG among unicyclic graph with girth k, respectively. As an application, the minimal and the maximal unicyclic graphs for some exponential VDB indices are achieved. In addition, we summarize our achievements and propose future research directions in the conclusion.

Suggested Citation

  • Zhenhua Su & Zikai Tang, 2025. "The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:4034455
    DOI: 10.1155/jom/4034455
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    References listed on IDEAS

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    1. Kinkar Chandra Das, 2025. "On the Exponential Atom-Bond Connectivity Index of Graphs," Mathematics, MDPI, vol. 13(2), pages 1-19, January.
    2. Li, Fengwei & Ye, Qingfang, 2024. "Extremal graphs with given parameters in respect of general ABS index," Applied Mathematics and Computation, Elsevier, vol. 482(C).
    3. Mondal, Sourav & Das, Kinkar Chandra, 2024. "Complete solution to open problems on exponential augmented Zagreb index of chemical trees," Applied Mathematics and Computation, Elsevier, vol. 482(C).
    4. Chen, Meng & Zhu, Yan, 2024. "Extremal unicyclic graphs of Sombor index," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    5. Gao, Wei & Gao, Yubin, 2024. "The extremal trees for exponential vertex-degree-based topological indices," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    6. Chen, Xiaohong, 2023. "General sum-connectivity index of a graph and its line graph," Applied Mathematics and Computation, Elsevier, vol. 443(C).
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