5 problems

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 $G_{k,r,s}$…

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

Weighted Laplacian Spread Conjecture. One has

Algebraic lower-bound conjecture. The pair $(x,y)$ satisfies