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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4 Pith papers cite this work. Polarity classification is still indexing.
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math.CO 4years
2026 4verdicts
UNVERDICTED 4representative citing papers
The authors prove that for a unicyclic graph G on n vertices with odd cycle length k, s+(G) > n > s-(G) when k ≡ 3 mod 4 and s+(G) < n < s-(G) when k ≡ 1 mod 4.
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.
Establishes path-minimality inequalities for adjacency p-energies, Laplacian-type spectral sums, and signless Laplacian energies of line graphs under stated conditions on p and graph class.
citing papers explorer
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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.
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A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs
The authors prove that for a unicyclic graph G on n vertices with odd cycle length k, s+(G) > n > s-(G) when k ≡ 3 mod 4 and s+(G) < n < s-(G) when k ≡ 1 mod 4.
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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.
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Path-Minimality for Positive $p$-Energies, Laplacian-Type Spectra, and Line Graphs
Establishes path-minimality inequalities for adjacency p-energies, Laplacian-type spectral sums, and signless Laplacian energies of line graphs under stated conditions on p and graph class.