A conjecture of eigenvalues of threshold graphs

Fernando Tura

A conjecture of eigenvalues of threshold graphs

Combinatorics 2020-06-08 v1

Authors: Fernando Tura

Abstract

Let $A_n$ be the anti-regular graph of order $n.$ It was conjectured that among all threshold graphs on $n$ vertices, $A_n$ has the smallest positive eigenvalue and the largest eigenvalue less than $-1.$ Recently, in \cite{Cesar2} was given partial results for this conjecture and identified the critical cases where a more refined method is needed. In this paper, we deal with these cases and confirm that conjecture holds.

Keywords

hadwiger conjecture graph laplacian random graphs

Cite

@article{arxiv.2006.03136,
  title  = {A conjecture of eigenvalues of threshold graphs},
  author = {Fernando Tura},
  journal= {arXiv preprint arXiv:2006.03136},
  year   = {2020}
}

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