For every p ≥ 2 and every connected simple graph G on n vertices, the p-energy E_p(G) is at least E_p(P_n), with equality for p > 2 if and only if G is the path.
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Path-Minimality of $p$-Energy for Connected Graphs
For every p ≥ 2 and every connected simple graph G on n vertices, the p-energy E_p(G) is at least E_p(P_n), with equality for p > 2 if and only if G is the path.