7 problems

Braga–Rodrigues–Trevisan conjecture.

Let $G$ be a graph with $n$ vertices, let $\overline{G}$ be its complement, and let $s_k(G)$ denote the sum of the $k$ largest Laplacian eigenvalues of $G$. Nordhaus–Gaddum full Br…

Let $G$ be a graph on $n$ vertices with $m$ edges and Laplacian eigenvalues $\mu_1\geq\mu_2\geq\cdots\geq\mu_n$, and define … For integers $k\in\{1,2,\cdots,n-1\}$, let $G_{k,r,s}$…

You–Liu–Zhai–Shu–Hong conjecture. For any graph $G$ on $n$ vertices,

SE$(s)$ extremal conjecture. The quantities $x$ and $y$ satisfy

Weighted Laplacian Spread Conjecture. One has

Dandelion extremal conjecture. The dandelion graph on $n$ vertices, together with its complement, minimizes