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ZIGZAG POLYHEX NANOTUBES WHICH ARE CAYLEY GRAPHS
Keywords:
Cayley graph, zigzag polyhex, regular group, automorphism group.DOI:
https://doi.org/10.17654/0974165822001Abstract
Iijima and Ichihashi [4] discovered single walled carbon nanotubes (SWCNs), which contain three different types of structures: zigzag, armchair and chiral. Denote by $\operatorname{TUHC}_6[p, q]$ the zigzag polyhex nanotube, in terms of the circumference $p$ and the length $q$. Cayley graph $C a y(G, S)$ on a group $G$ with connection set $S$ has the elements of $G$ as its vertices and an edge joining $g$ and $s g$ for all $g \in S$ and $s \in S$. Motivated by Afshari and Maghasedi's [1] work and Hamada et al.'s [10] notation, we show that the zigzag polyhex nanotubes $\Gamma=T_{U H C}^6[n, n]$ are Cayley graphs by constructing a regular subgroup of $A u t(\Gamma)$.
Received: August 18, 2021
Accepted: October 4, 2021
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