| Title: | Nut digraphs |
|---|
| Authors: | ID Bašić, Nino (Author)
ID Fowler, Patrick W. (Author)
ID McCarthy, Maxine M. (Author)
ID Potočnik, Primož (Author) |
|---|
| Files: |  RAZ_Basic_Nino_2026.pdf (873,25 KB)
MD5: D28F9C22CE19D03C7054F6E2F7513F0F
 https://www.sciencedirect.com/science/article/pii/S0166218X25007498?via%3Dihub
|
|---|
| Language: | English |
|---|
| Work type: | Unknown |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
|
|---|
| Abstract: | A nut graph is a simple graph whose kernel is spanned by a single full vector (i.e., the adjacency matrix has a single zero eigenvalue and all non-zero kernel eigenvectors have no zero entry). We classify generalisations of nut graphs to nut digraphs: a digraph whose kernel (resp. co-kernel) is spanned by a full vector is dextro-nut (resp. laevo-nut); a bi-nut digraph is both laevo- and dextro-nut; an ambi-nut digraph is a bi-nut digraph where kernel and co-kernel are spanned by the same vector; a digraph is inter-nut if the intersection of the kernel and co-kernel is spanned by a full vector. It is known that a nut graph is connected, leafless and non-bipartite. It is shown here that an ambi-nut digraph is strongly connected, non-bipartite (i.e., has a non-bipartite underlying graph) and has minimum in-degree and minimum out-degree of at least 2. Refined notions of core and core-forbidden vertices apply to singular digraphs. Infinite families of nut digraphs and systematic coalescence, crossover and multiplier constructions are introduced. Relevance of nut digraphs to topological physics is discussed. |
|---|
| Keywords: | nut graph, core graph, nullity, directed graph, nut digraph, dextro-nut, laevo-nut, bi-nut, ambi-nut, inter-nut, dextro-core vertex, laevo-core vertex, graph spectra |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 15.04.2026 |
|---|
| Year of publishing: | 2026 |
|---|
| Number of pages: | str. 203-226 |
|---|
| Numbering: | Vol. 383 |
|---|
| PID: | 20.500.12556/RUP-22450  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 0166-218X |
|---|
| DOI: | 10.1016/j.dam.2025.12.037 |
|---|
| COBISS.SI-ID: | 264177411 |
|---|
| Publication date in RUP: | 09.01.2026 |
|---|
| Views: | 149 |
|---|
| Downloads: | 3 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
