The cyclic graph (deleted enhanced power graph) of a direct product
The cyclic graph (deleted enhanced power graph) of a direct product
Let $G$ be a finite group. Define a graph on the set $G^{\#} = G \setminus \{ 1 \}$ by declaring distinct elements $x,y\in G^{\#}$ to be adjacent if and only if $\langle x,y\rangle$ is cyclic. Denote this graph by $\Delta(G)$. The graph $\Delta(G)$ has appeared in the literature under …