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<p>Let <i>G</i>(<i>n</i>,&#xa0;<i>k</i>) be the class of clique trees on <i>n</i> vertices and zero forcing number <i>k</i>, where <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3269_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="150" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left\lfloor \frac{n}{2} \right\rfloor + 1 \le k \le n-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close="⌋" open="⌊"> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> </mfenced> <mo>+</mo> <mn>1</mn> <mo>≤</mo> <mi>k</mi> <mo>≤</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and each block is a clique of size at least 3. In this article, we proved the uniqueness of a clique tree in <i>G</i>(<i>n</i>,&#xa0;<i>k</i>) that attains maximal spectral radius among all graphs in <i>G</i>(<i>n</i>,&#xa0;<i>k</i>). We also provide an upper bound for the spectral radius of the extremal graph.</p>

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On the maximum spectral radius of clique trees with a given zero forcing number

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Joyentanuj Das

摘要

Let G(n, k) be the class of clique trees on n vertices and zero forcing number k, where \(\left\lfloor \frac{n}{2} \right\rfloor + 1 \le k \le n-1\) n 2 + 1 ≤ k ≤ n - 1 and each block is a clique of size at least 3. In this article, we proved the uniqueness of a clique tree in G(n, k) that attains maximal spectral radius among all graphs in G(n, k). We also provide an upper bound for the spectral radius of the extremal graph.