5 problems

Let $G$ and $H$ be non-abelian finite groups, and suppose their non-commuting graphs are isomorphic. Abdollahi et al.'s order conjecture. Then … This conjecture concerns whether th…

Class 1 conjecture. The relative non-commuting graph $\Gamma_{S,R}$ is of class $1$.

Order conjecture for irregular non-commuting graphs. If one of $G$ and $H$ is nilpotent and

Order-determination conjecture. If

Let $q$ be a prime power and let ${\rm GL}_n(q)$ denote the finite general linear group of degree $n$ over the field with $q$ elements. Let $\omega(G)$ denote the maximum cardinali…