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

DOI: https://doi.org/10.37236/6541

Keywords: Cayley graph, CI-group, Isomorphism

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

$3p$ .