6 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…

Let $G$ be a graph, and let $n^+(G)$ and $n^-(G)$ denote the numbers of positive and negative eigenvalues of its adjacency matrix, counted with multiplicity. Akbari–Elphick–Kumar–P…

Kwan–Wigderson's conjecture. With high probability,

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…