Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions

Domingos M. Cardoso; Inês Serôdio Costa; Rui Duarte

Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions

Combinatorics 2022-02-25 v4

Authors: Domingos M. Cardoso , Inês Serôdio Costa , Rui Duarte

Abstract

Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the $n$ -Queens' graph $\mathcal{Q}(n)$ is equal to $-4$ for every $n \ge 4$ and it is also proven that the multiplicity of this eigenvalue is $(n-3)^2$ . Additionally, some results on the edge clique partition graph parameters are obtained.

Keywords

graph least eigenvalue edge clique partition sharp bounds n-queens graph eigenvalue multiplicity

Cite

@article{arxiv.2201.01224,
  title  = {Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions},
  author = {Domingos M. Cardoso and Inês Serôdio Costa and Rui Duarte},
  journal= {arXiv preprint arXiv:2201.01224},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2012.01992

Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions

Abstract

Keywords

Cite

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