H_{n,a} maximizes both edge count and spectral radius among all non-[a,b]-covered graphs.
Nikiforov, The spectral radius of graphs without paths and cycles of specified length,Linear Algebra Appl.432(2010) 2243-2256
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Extremal problems on $[a, b]$-covered graphs
H_{n,a} maximizes both edge count and spectral radius among all non-[a,b]-covered graphs.