English

The largest eigenvalue of $\mathcal{C}_4^{-}$-free signed graphs

Combinatorics 2023-09-11 v1

Abstract

Let Ck\mathcal{C}_{k}^{-} be the set of all negative CkC_k. For odd cycle, Wang, Hou and Li [29] gave a spectral condition for the existence of negative C3C_3 in unbalanced signed graphs. For even cycle, we determine the maximum index among all C4\mathcal{C}_4^{-}-free unbalanced signed graphs and completely characterize the extremal signed graph in this paper. This could be regarded as a signed graph version of the results by Nikiforov [23] and Zhai and Wang [37].

Keywords

Cite

@article{arxiv.2309.04101,
  title  = {The largest eigenvalue of $\mathcal{C}_4^{-}$-free signed graphs},
  author = {Yongang Wang and Huiqiu Lin},
  journal= {arXiv preprint arXiv:2309.04101},
  year   = {2023}
}
R2 v1 2026-06-28T12:15:53.134Z