Analytical eigenspectra of alternant edge-weighted graphs of linear chains and cycles: some applications

Abstract

Analytical eigenspectra for the graphs of linear chains and cycles with alternant edge weights has been derived with the use of two independent methods, namely, the characteristic polynomial and the graph squaring. In the former method the rotational symmetry and the trigonometric identity have been exploited. These methods along with the expressions of eigenspectra so obtained have been found to be very useful in expressing analytical eigensolutions of some important as well as novel benzenoids, for example, linear p-methylene poly(p-phenylene), cylindrical poly(p-phenylene), zigzag edge graphene, carbon nanotube and carbon nanotori. Some of these eigensolutions have been analysed in exploring some consequences thereof.

Keywords:

• alternant edge-weighted graphs
• graph eigenspectra
• poly(p-phenylene)
• zigzag edge graphene
• carbon nanotube and nanotori

Acknowledgements

Authors are thankful to the learned referees for their valuable comments.

Additional information

Funding

The authors acknowledge the support [grant number BD-0894] from the Welch Foundation of Houston, Texas.