Trivial diameter bound for a finite group
= Trivial diameter bound for a finite group
A connected <Cayley graph> on a finite group $G$ has $|G|$ vertices, and a shortest path repeats no vertex. Therefore
$$
\operatorname{diam}_S(G)\leq|G|-1.
$$
= Trivial diameter bound for a finite group
A connected <Cayley graph> on a finite group $G$ has $|G|$ vertices, and a shortest path repeats no vertex. Therefore
$$
\operatorname{diam}_S(G)\leq|G|-1.
$$