Classification of cubic tricirculant nut graphs

Damnjanović, Ivan (author), Bašić, Nino (author), Pisanski, Tomaž (author), Žitnik, Arjana (author)

A nut graph is a simple graph whose adjacency matrix has the eigenvalue zero with multiplicity one such that its corresponding eigenvector has no zero entries. It is known that there exist no cubic circulant nut graphs. A bicirculant (resp. tricirculant) graph is defined as a graph that admits a cyclic group of automorphisms having two (resp. three) orbits of vertices of equal size. We show that there exist no cubic bicirculant nut graphs and we provide a full classification of cubic tricirculant nut graphs.

• Language: English
• Keywords: bicirculant, tricirculant, eigenvalue
• 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: 01.01.2024
• Year: 2024
• Number of pages: Str. 1-32
• Numbering: Vol. 31, iss. 2, article no. P2.31
• PID: 20.500.12556/RUL-166785
• UDC: 519.17
• ISSN on article: 1077-8926
• DOI: 10.37236/12668
• COBISS.SI-ID: 217572099
• Publication date in RUL: 24.01.2025

Record is a part of a journal

• Title: The Electronic journal of combinatorics
• Shortened title: Electron. j. comb.
• Publisher: N.J. Calkin and H.S. Wilf
• ISSN: 1077-8926
• COBISS.SI-ID: 6973785

Licences

• License: CC BY-ND 4.0, Creative Commons Attribution-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nd/4.0/
• Description: Under the NoDerivatives Creative Commons license one can take a work released under this license and re-distribute it, but it cannot be shared with others in adapted form, and credit must be provided to the author.

Secondary language

• Language: Slovenian
• Keywords: bicirkulant, tricirkulant, lastna vrednost