Some New Groups which are not CI-groups with Respect to Graphs

Abstract

A group $G$ is a CI-group with respect to graphs if two Cayley graphs of $G$ are isomorphic if and only if they are isomorphic by a group automorphism of $G$.  We show that an infinite family of groups which include $D_n\times F_{3p}$ are not CI-groups with respect to graphs, where $p$ is prime, $n\not = 10$ is relatively prime to $3p$, $D_n$ is the dihedral group of order $n$, and $F_{3p}$ is the nonabelian group of order $3p$.