The high order spectral extrema of $2K_r$-free graphs

Changjiang Bu; Yifan Sun; Haotian Zeng

The high order spectral extrema of $2K_r$-free graphs

Combinatorics 2026-04-22 v1

Authors: Changjiang Bu , Yifan Sun , Haotian Zeng

Abstract

In this paper, we determine the graphs with maximum value of the sum number from $k$ -clique spectral radius to $(2r-1)$ -clique spectral radius among all $2K_{r}$ -free graphs on $n$ vertices for $r\le k$ and large $n$ . We also determine the graphs with maximum $3$ -clique spectral radius among all $2K_{3}$ -free graphs on $n$ vertices. Our results are spectral versions of some results on generalized Tur\'an numbers.

Keywords

spectral extremal graph theory clique spectral radius 2K_r-free graph generalized Turán number

Cite

@article{arxiv.2604.19409,
  title  = {The high order spectral extrema of $2K_r$-free graphs},
  author = {Changjiang Bu and Yifan Sun and Haotian Zeng},
  journal= {arXiv preprint arXiv:2604.19409},
  year   = {2026}
}

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