10 problems

List distinguishing index conjecture.

Let $G$ be a finite connected graph on at least six vertices, and let $D'_s(G)$ denote the minimum number of edge colours needed to break every small automorphism of $G$. Kalinowsk…

Conjecture for distinguishing index two. If

Lower-bound conjecture.

Let $\kappa$ be an infinite cardinal, and let $G$ be a connected $\kappa$-regular graph. Distinguishing-index conjecture. The distinguishing index of $G$ is at most $\kappa$. The p…

Let $G$ be a regular graph among the graphs remaining after the cases established in the paper have been excluded, and let $D'(G)$ denote its distinguishing index, the minimum numb…

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