8 problems

DGA$_\alpha$-spectral determination conjecture. If $G\in\mathfrak{F}_n$, $n$ is even, and $c_\alpha\geqslant 3$ is odd, then $G$ is DGA$_\alpha$S.

Let $G_1$ and $G_2$ be graphs with $B_1\subseteq V(G_1)$ and $B_2\subseteq V(G_2)$. Coalescing conjecture. If coalescing the same connected rooted graph onto every vertex of $B_1$…

Diagonalizability conjecture. Every vertex-primitive arc-transitive digraph is diagonalizable.

Dehmer–Pickl–Shi–Yu conjecture. For every such pair of trees,

Dehmer–Pickl–Shi–Yu conjecture. For every such pair of trees,

Let $K_r$ be the complete graph on $r$ vertices, let $sK_t$ be the disjoint union of $s$ copies of $K_t$, and let $K_r\triangledown sK_t$ denote their join. A graph is determined b…

Downer-vertex conjecture. In any chain graph, every vertex is downer with respect to every non-zero eigenvalue.

Let $\Gamma$ be a finite subgroup of $GL(2,\mathbb{Z})$, let $(\mathcal{G}^{\Gamma}_{\rho_1},\mathcal{G}^{\Gamma}_{\rho_2})$ be the associated pair of graphs, let $\mathbb{T}^2$ be…