6 problems

For a graph $G$, define its Laplacian energy by … where $L(G)$ is the Laplacian matrix and $\lambda_i(L(G))$ are its eigenvalues. Let $P_n$ be the path on $n$ vertices. Radenković–…

For a graph $G$ on $n$ vertices, let … where $L(G)$ is the Laplacian matrix and $\lambda_i(L(G))$ are its eigenvalues. Radenković–Gutman's Laplacian energy conjecture. Among all tr…

Laplacian energy conjecture.

Maximal Laplacian energy conjecture. The graph $H_n$ has maximum Laplacian energy among all graphs on $n$ vertices.

Pineapple conjecture. Among all connected graphs on $n$ vertices, the pineapple maximizes the Laplacian energy.

Spectral threshold dominance conjecture. All graphs are spectrally threshold dominated.