For p ≥ 2 the p-energy of any connected graph on n vertices is minimized by the path P_n, with equality only for the path when p > 2.
Davis, All convex invariant functions of hermitian matrices,Archiv der Mathematik8(1957), 276–278
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Path-Minimality of $p$-Energy for Connected Graphs
For p ≥ 2 the p-energy of any connected graph on n vertices is minimized by the path P_n, with equality only for the path when p > 2.