3 problems

Spectral approximation conjecture. The normalized eigenvalue-counting functions converge to the spectral density function:

Convergence to the null graph conjecture. The iterates satisfy

Let $G$ be a graph of order $n\ge 2$, and let $L(G)$ and $M(G)$ denote its line graph and middle graph, respectively. The line-middle graph inequality conjecture asserts that … The…