- Tytuł:
- On Singular Signed Graphs with Nullspace Spanned by a Full Vector: Signed Nut Graphs
- Autorzy:
-
Bašić, Nino
Fowler, Patrick W.
Pisanski, Tomaž
Sciriha, Irene - Powiązania:
- https://bibliotekanauki.pl/articles/32222533.pdf
- Data publikacji:
- 2022-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
signed graph
nut graph
singular graph
graph spectrum
Fowler construction
sign-balanced graph
sign-unbalanced graph
cocktail-party graph - Opis:
- 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 sign-unbalanced 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1351-1382
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł