4 problems

Let $G$ be a graph of order $n$, and let $n^+(G)$ denote the number of positive eigenvalues of its adjacency matrix, counted with multiplicity. Akbari–Elphick–Kumar–Pragada–Tang's…

Unweighted Nordhaus–Gaddum conjecture. One has

Kwan–Wigderson's conjecture. For every integer $k$, there exists a graph $G$ with $\alpha(G)=2$ and

Let $G$ be a simple graph with adjacency matrix $A(G)$. Its signature is $s(G)=p(G)-n(G)$, where $p(G)$ and $n(G)$ are respectively the numbers of positive and negative eigenvalues…