Random walks and the electronic structure of graphene

Bašić, Nino (author), Fowler, Patrick W. (author), Pickup, Barry T. (author), Potočnik, Primož (author)

Results from the mathematical literature on random walks reveal a closed-form analytical expression for the $\pi$-energy and bond number of graphene in the simplest tight-binding model and its Hartree-Fock Hubbard extension. Closed-form expressions follow for all $\pi$ spectral moments of graphene. Bond numbers of carbon and boron nitride (BN) zigzag nanotubes are found as finite sums, with graphene and hexagonal boron nitride sheets as asymptotes.

• Language: English
• Keywords: graph theory, random walks, graphene, bond number
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2026
• Year: 2026
• Number of pages: Str. 104103-1-104103-6
• Numbering: Vol. 164, iss. 10
• PID: 20.500.12556/RUL-180466
• UDC: 519.17:54
• ISSN on article: 0021-9606
• DOI: 10.1063/5.0319282
• COBISS.SI-ID: 271072515
• Publication date in RUL: 10.03.2026

Record is a part of a journal

• Title: The Journal of chemical physics
• Shortened title: J. chem. phys.
• Publisher: American Institute of physics
• ISSN: 0021-9606
• COBISS.SI-ID: 5253893

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: teorija grafov, slučajni sprehodi, grafen, število vezi

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0294
• Name: Računsko intenzivne metode v teoretičnem računalništvu, diskretni matematiki, kombinatorični optimizaciji ter numerični analizi in algebri z uporabo v naravoslovju in družboslovju