Signed graphs with maximal index

Ebrahim Ghorbani; Arezoo Majidi

Signed graphs with maximal index

Combinatorics 2021-05-04 v2

Authors: Ebrahim Ghorbani , Arezoo Majidi

Abstract

The index of a signed graph is the largest eigenvalue of its adjacency matrix. For positive integers $n$ and $m\le n^2/4$ , we determine the maximal index of complete signed graphs with $n$ vertices and $m$ negative edges. This settles (the corrected version of) a conjecture by Koledin and Stani\'c (2017).

Keywords

graph laplacian graph theory graph pebbling

Cite

@article{arxiv.2101.01503,
  title  = {Signed graphs with maximal index},
  author = {Ebrahim Ghorbani and Arezoo Majidi},
  journal= {arXiv preprint arXiv:2101.01503},
  year   = {2021}
}

Comments

14 pages, final version, to appear in Discrete Mathematics

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