7 problems

Conjecture for distinguishing index two. If

Lower-bound conjecture.

List distinguishing index conjecture.

Pilsniak's conjecture.

Let $G$ be a $k$-regular graph, meaning that every vertex of $G$ has degree $k$. The distinguishing index of $G$, denoted $D'(G)$, is the least number of edge labels needed so that…

Proposed distinguishing-index conjecture. (i) If $G$ is a $\delta$-minimally graph with $\delta(G)\geq 3$ and $G$ is neither a complete bipartite graph nor a $\delta$-regular graph…

Piśniak's conjecture. If $G$ is a $2$-connected graph, then