- Tytuł:
- Existence of Regular Nut Graphs for Degree at Most 11
- Autorzy:
-
Fowler, Patrick W.
Gauci, John Baptist
Goedgebeur, Jan
Pisanski, Tomaž
Sciriha, Irene - Powiązania:
- https://bibliotekanauki.pl/articles/31550028.pdf
- Data publikacji:
- 2020-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
nut graph
core graph
regular graph
nullity - Opis:
- A nut graph is a singular graph with one-dimensional kernel and corresponding eigenvector with no zero elements. The problem of determining the orders n for which d-regular nut graphs exist was recently posed by Gauci, Pisanski and Sciriha. These orders are known for d ≤ 4. Here we solve the problem for all remaining cases d ≤ 11 and determine the complete lists of all d-regular nut graphs of order n for small values of d and n. The existence or non-existence of small regular nut graphs is determined by a computer search. The main tool is a construction that produces, for any d-regular nut graph of order n, another d-regular nut graph of order n+2d. If we are given a sufficient number of d-regular nut graphs of consecutive orders, called seed graphs, this construction may be applied in such a way that the existence of all d-regular nut graphs of higher orders is established. For even d the orders n are indeed consecutive, while for odd d the orders n are consecutive even numbers. Furthermore, necessary conditions for combinations of order and degree for vertex-transitive nut graphs are derived.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 533-557
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł