3 problems

Let $r$ be a positive integer. Let $M_X$ be an $m\times r$ integer matrix and let $X=M_X^{SACG}$ denote the Abelian Cayley graph associated with $M_X$. Assume that $M_X$ has no zer…

Let $G$ be a graph, let $p\geq 2$, and let $\chi_v(G)$ denote its vector chromatic number. Let $\mathcal{E}_p^+(G)$ and $\mathcal{E}_p^-(G)$ denote its positive and negative $p$-en…

Let $G$ be a connected graph with $n$ vertices, and let $\mathcal{E}_p^+(G)$ and $\mathcal{E}_p^-(G)$ denote its positive and negative $p$-energies. Elphick–Wocjan conjecture. For…