Undirected power graph of a group

Definition

Let $G$ be a group. The undirected power graph of $G$ is the graph whose vertices are the elements of $G$ and where, given two distinct vertices $g$ and $h$, there is an edge between $g$ and $h$ if either $g$ is a power of $h$ or $h$ is a power of $g$.

Related notions

• Directed power graph of a group

Facts

• Undirected power graph determines directed power graph for finite group
• Finite groups are 1-isomorphic iff their directed power graphs are 1-isomorphic