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<p>The study of graph complexity has led to a deeper understanding of the structures of graphs. This paper presents new findings on the Szeged complexity of graphs. Specifically, we prove that for bipartite graphs on <i>n</i> vertices, the upper bound of Szeged complexity is <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3159_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lfloor \frac{n}{2} \rfloor \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>⌊</mo> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> <mo>⌋</mo> </mrow> </math></EquationSource> </InlineEquation>. Moreover, we establish that the lower bound of Szeged complexity of a tree <i>T</i> is the radius of <i>T</i>. Furthermore, we characterize trees with Szeged complexity three and determine their Wiener complexity.</p>

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Complexity measures in trees: a comparative investigation of Szeged and Wiener indices

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Modjtaba Ghorbani,
  • Zahra Vaziri,
  • Matthias Dehmer

摘要

The study of graph complexity has led to a deeper understanding of the structures of graphs. This paper presents new findings on the Szeged complexity of graphs. Specifically, we prove that for bipartite graphs on n vertices, the upper bound of Szeged complexity is \(\lfloor \frac{n}{2} \rfloor \) ⌊ n 2 ⌋ . Moreover, we establish that the lower bound of Szeged complexity of a tree T is the radius of T. Furthermore, we characterize trees with Szeged complexity three and determine their Wiener complexity.