5 problems

Normalized algebraic-connectivity conjecture.

Let $G$ be a graph on $n$ vertices, and let $\lambda_2(G)$ denote the second-smallest eigenvalue of its normalized Laplacian. Connected-complement normalized Laplacian conjecture.…

Let $G$ be a graph on $n\geq5$ vertices, with normalized Laplacian eigenvalues $0=\lambda_1(G)\leq\lambda_2(G)\leq\cdots\leq\lambda_n(G)$. Normalized Laplacian maximum-bound conjec…

Normalized Laplacian maximum-connectivity conjecture.

Let $G$ be a graph, let $x,y$ be vertices, and let $\lambda$ be an eigenvalue of the normalized Laplacian whose edge derivative is being considered. The edge derivative with respec…