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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, Hindawi, vol. 2025, pages 1-9, March.
    • Handle: RePEc:hin:jjmath:4034455
    DOI: 10.1155/jom/4034455
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