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

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

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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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Bibliographic Details
Main Author: Zoran Stanić
Format: Article
Language:English
Published: American Journal of Combinatorics 2022-12-01
Series:The American Journal of Combinatorics
Subjects:
Signed graph
Adjacency matrix
Largest eigenvalue
Frustration index
Vertex degree
Spanning subgraph
Online Access:https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/7

Internet

https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/7

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