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Maximal Spectral Radius of Minimally k k‐(Edge)‐Connected Graphs

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This research shows the unique extremal graph for fixed sizes, highlighting spectral radius in minimally connected graphs.

The study identifies the unique extremal graph for minimally edge-connected graphs with fixed edges, providing a complete solution to the problem.
Prior conjectures on spectral radius and connected graphs are addressed, reinforcing earlier findings from 1988 by Rowlinson about graph transformation.
Schmidt's earlier work confirmed tight bounds on vertex degrees in minimally connected graphs, setting the stage for this research.
The methodology relies on double eigenvector transformations, affirming their importance in solving extremal graph problems.

Zhai et al. (2025) studied this question.

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