Spectral Tur\'an problem for $t\mathcal{K}_{4}^{-}$-free unbalanced signed graphs

Linfeng Xie; Xiaogang Liu

Spectral Tur\'an problem for $t\mathcal{K}_{4}^{-}$-free unbalanced signed graphs

Combinatorics 2026-04-14 v1

Authors: Linfeng Xie , Xiaogang Liu

Abstract

Let $tK_4$ denote the family of all graphs consisting of $t$ copies of $K_4$ that are allowed to share vertices and $t\mathcal{K}_{4}^{-}$ be the set of all unbalanced signed graphs whose underlying graphs are elements of $tK_4$ . In this paper, we characterize the extremal graphs that achieve the maximum index and spectral radius among all $t\mathcal{K}_{4}^{-}$ -free unbalanced signed graphs with given order.

Keywords

spectral graph theory graph theory

Cite

@article{arxiv.2604.11428,
  title  = {Spectral Tur\'an problem for $t\mathcal{K}_{4}^{-}$-free unbalanced signed graphs},
  author = {Linfeng Xie and Xiaogang Liu},
  journal= {arXiv preprint arXiv:2604.11428},
  year   = {2026}
}

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