Some relations between the largest eigenvalue and the frustration index of a signed graph

Let \(\dot{G}\) be a signed graph with \(n\) vertices and the frustration index \(\ell\). We prove the existence of \(k~(k\geq \ell)\) edges \(e_1, e_2, \ldots, e_k\) of \(\dot{G}\) such that \[\begin{equation*}\lambda_1(\dot{G})\leq \lambda_1(\dot{G}-e_1)\leq \lambda_1(\dot{G}-e_1-e_2)\leq\cdots\l...

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Detalhes bibliográficos

Autor principal:	Zoran Stanić
Formato:	Artigo
Idioma:	Inglês
Publicado em:	American Journal of Combinatorics 2022-12-01
coleção:	The American Journal of Combinatorics
Assuntos:	Signed graph Adjacency matrix Largest eigenvalue Frustration index Vertex degree Spanning subgraph
Acesso em linha:	https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/7
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