@article{Wang2026, 
author = {Guangfu Wang and Chunxiao Xu and Wenchao Cong},
title = {l    1  -embeddability of pentagon-based open-ended nanotubes and its applications},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {12934-12960},
keywords = {l1-graph, zigzag pentagon-based nanotubes, armchair pentagon-based nanotubes, the Wiener index},
url = {https://www.sciopen.com/article/10.3934/math.2026532},
doi = {10.3934/math.2026532},
abstract = {A graph is        l    1  -embeddable if it admits a binary addressing such that the Hamming distance between the binary addresses is, up to scale, the distance in the graph between the corresponding vertices. The zigzag pentagon-based nanotubes and armchair pentagon-based nanotubes are two new materials with the tube shapes. In order to easily calculate their chemical indices based on distances, we showed that only five types        I    (  p  ,  1  ),        I    (  1  ,  q  ,  θ  ) with    q  ≥  5,    I  (  1  ,  3  ,  θ  ),    I  (  2  ,  3  ,  ζ  ) and    I  (  2  ,  5  ,  ζ  ) zigzag pentagon-based nanotubes were        l    1  -embeddable. Finally, we gave the precise value of the Wiener index and the hyper-Wiener index of these five zigzag pentagon-based nanotubes.}
}