7 problems

Let $G$ be a connected graph on $n$ vertices. Define its positive and negative square energies by … where $\lambda_1,\ldots,\lambda_n$ are the adjacency eigenvalues of $G$. Elphick…

Elphick–Wocjan conjecture. For every graph $G$ on $n\ge 1$ vertices,

Let $G$ be a connected graph on $n$ vertices, and let $p$ satisfy $0\leq p\leq 2$. Let $\mathcal{E}_p^+(G)$ and $\mathcal{E}_p^-(G)$ denote the positive and negative $p$-energies o…

Let $n$ and $p$ be positive integers with $p\geq 2$, let $G$ be a connected graph on $n$ vertices, and let $K_n$ denote the complete graph on $n$ vertices. Akbari–Kumar–Mohar's neg…

Let $n$ and $p$ be positive integers with $p\geq 2$, let $G$ be a connected graph on $n$ vertices, and let $P_n$ denote the path on $n$ vertices. Tang–Liu–Wang's positive $p$-energ…

Let $G$ be a connected graph on $n$ vertices, and let $\mathcal{E}_2^+(G)$ and $\mathcal{E}_2^-(G)$ denote its positive and negative $2$-energies, respectively. Elphick–Tang–Zhang'…

Let $(\pi,\phi)$ be a recurrent virtual graph endomorphism, and for $q\in[1,\infty]$ let $\overline{E}{}^q[\pi,\phi]$ denote its asymptotic $q$-conformal graph energy. Strict-decre…