Please use this identifier to cite or link to this item:
https://www.um.edu.mt/library/oar/handle/123456789/116208
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bašić, Nino | - |
dc.contributor.author | Fowler, Patrick W. | - |
dc.contributor.author | Pisanski, Tomaz | - |
dc.contributor.author | Sciriha, Irene | - |
dc.date.accessioned | 2023-12-04T10:58:23Z | - |
dc.date.available | 2023-12-04T10:58:23Z | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | Bašić, N., Fowler, P. W., Pisanski, T., & Sciriha, I. (2022). On singular signed graphs with nullspace spanned by a full vector: signed nut graphs. Discussiones Mathematicae Graph Theory, 42(4), 1351-1382. | en_GB |
dc.identifier.uri | https://www.um.edu.mt/library/oar/handle/123456789/116208 | - |
dc.description.abstract | A signed graph has edge weights drawn from the set {+1, −1}, and is sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwise it is sign-unbalanced. A nut graph has a one dimensional kernel of the 0-1 adjacency matrix with a corresponding eigenvector that is full. In this paper we generalise the notion of nut graphs to signed graphs. Orders for which regular nut graphs with all edge weights +1 exist have been determined recently for the degrees up to 12. By extending the definition to signed graphs, we here find all pairs (ρ, n) for which a ρ-regular nut graph (sign-balanced or sign-unbalanced) of order n exists with ρ ≤ 11. We devise a construction for signed nut graphs based on a smaller ‘seed’ graph, giving infinite series of both sign-balanced and signunbalanced ρ-regular nut graphs. Orders for which a regular nut graph with ρ = n − 1 exists are characterised; they are sign-unbalanced with an underlying graph Kn for which n ≡ 1 (mod 4). Orders for which a regular sign-unbalanced nut graph with ρ = n−2 exists are also characterised; they have an underlying cocktail-party graph CP(n) with even order n ≥ 8. | en_GB |
dc.language.iso | en | en_GB |
dc.publisher | Uniwersytet Zielonogorski * Wydzial Matematyki, Informatyli i Ekonometrii,Technical University Zielona Gora, Institute of Mathematic | en_GB |
dc.rights | info:eu-repo/semantics/openAccess | en_GB |
dc.subject | Graph theory | en_GB |
dc.subject | Kernel functions | en_GB |
dc.subject | Graph algorithms | en_GB |
dc.subject | Nullity | en_GB |
dc.subject | Eigenvalues | en_GB |
dc.title | On singular signed graphs with nullspace spanned by a full vector : signed nut graphs | en_GB |
dc.type | article | en_GB |
dc.rights.holder | The copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder. | en_GB |
dc.description.reviewed | peer-reviewed | en_GB |
dc.publication.title | Discussiones Mathematicae Graph Theory | en_GB |
Appears in Collections: | Scholarly Works - FacSciMat |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
On singular signed graphs with nullspace spanned by a full vector signed nut graphs 2022.pdf | 472.63 kB | Adobe PDF | View/Open |
Items in OAR@UM are protected by copyright, with all rights reserved, unless otherwise indicated.