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<p>Let ex(<i>n</i>, <i>F</i>) and spex(<i>n</i>, <i>F</i>) be the maximum size and spectral radius among all <i>F</i>-free graphs with fixed order <i>n</i>, respectively. A fan is a graph <i>P</i><sub>1</sub> ∨ <i>P</i><sub><i>s</i></sub> (join of a vertex and a path of order <i>s</i>) for <i>s</i> ≥ 3, and it is called an even fan if <i>s</i> is even. In this paper, we study ex(<i>n, t</i>(<i>P</i><sub>1</sub> ∨ <i>P</i><sub>2<i>k</i></sub>)), spex(<i>n, t</i>(<i>P</i><sub>1</sub> ∨ <i>P</i><sub>2<i>k</i></sub>)) with <i>t</i> ≥ 1 and <i>k</i> ≥ 3 and characterize the corresponding extremal graphs for sufficiently large <i>n</i>.</p>

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Ordinary and Spectral Extremal Problems on Vertex Disjoint Copies of Even Fans

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Yiting Cai,
  • Bo Zhou

摘要

Let ex(n, F) and spex(n, F) be the maximum size and spectral radius among all F-free graphs with fixed order n, respectively. A fan is a graph P1 ∨ Ps (join of a vertex and a path of order s) for s ≥ 3, and it is called an even fan if s is even. In this paper, we study ex(n, t(P1 ∨ P2k)), spex(n, t(P1 ∨ P2k)) with t ≥ 1 and k ≥ 3 and characterize the corresponding extremal graphs for sufficiently large n.