Signed graphs with maximal index
Ebrahim Ghorbani, Arezoo Majidi

TL;DR
This paper determines the maximum eigenvalue of signed graphs with given size and negative edges, settling a conjecture and advancing spectral graph theory.
Contribution
It provides the exact maximum index for complete signed graphs with specified negative edges, resolving a conjecture by Koledin and Stanić.
Findings
Maximal index for complete signed graphs with given parameters identified
Conjecture by Koledin and Stanić confirmed and corrected
Advances understanding of spectral properties of signed graphs
Abstract
The index of a signed graph is the largest eigenvalue of its adjacency matrix. For positive integers and , we determine the maximal index of complete signed graphs with vertices and negative edges. This settles (the corrected version of) a conjecture by Koledin and Stani\'c (2017).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
