A counterexample to a conjecture of Wang and Hou on signed graphs

TL;DR

This paper presents a counterexample to a conjecture by Wang and Hou concerning the sum of the largest Laplacian eigenvalues in signed graphs, challenging previous assumptions in spectral graph theory.

Contribution

The authors provide the first known counterexample to Wang and Hou's conjecture, advancing understanding of eigenvalue sums in signed graph Laplacians.

Findings

Counterexample disproves the conjecture

Highlights limitations of existing spectral bounds

Suggests need for revised theoretical frameworks

Abstract

We give a counterexample to a conjecture of Wang and Hou related with the sum of the $k$ largest Laplacian eigenvalues of signed graphs.