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.
Extremal values for the square energies of graphs.arXiv preprint
2 Pith papers cite this work. Polarity classification is still indexing.
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Proves E^+_3(G) >= (sqrt(5)/2)n for connected n-vertex graphs except K1, K2, P3, and proves E^-_p(G) >= E^-_p(K_n) for all p >= 3.
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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.
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Positive and negative 3-energies of graphs
Proves E^+_3(G) >= (sqrt(5)/2)n for connected n-vertex graphs except K1, K2, P3, and proves E^-_p(G) >= E^-_p(K_n) for all p >= 3.