Iijima and Ichihashi [4] discovered single walled carbon nanotubes (SWCNs), which contain three different types of structures: zigzag, armchair and chiral. Denote by  the zigzag polyhex nanotube, in terms of the circumference p and the length q. Cayley graph  on a group G with connection set S has the elements of G as its vertices and an edge joining g and sg for all  and  Motivated by Afshari and Maghasedi’s [1] work and Hamada et al.’s [10] notation, we show that the zigzag polyhex nanotubes  are Cayley graphs by constructing a regular subgroup of

Cayley graph, zigzag polyhex, regular group, automorphism group