| Title: | Nut digraphs |
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| Authors: | ID Bašić, Nino (Author)
ID Fowler, Patrick W. (Author)
ID McCarthy, Maxine M. (Author)
ID Potočnik, Primož (Author) |
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| Files: |  PDF - Presentation file, download (1,26 MB)
MD5: AE85AB9366AC47B027F64C71307A3E0D
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0166218X25007498
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. |
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| 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 |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 15.04.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 203-226 |
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| Numbering: | Vol. 383 |
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| PID: | 20.500.12556/DiRROS-28058  |
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| UDC: | 519.17 |
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| ISSN on article: | 0166-218X |
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| DOI: | 10.1016/j.dam.2025.12.037 |
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| COBISS.SI-ID: | 264177411 |
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| Note: |
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| Publication date in DiRROS: | 09.03.2026 |
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| Views: | 252 |
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| Downloads: | 152 |
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| Metadata: |    |
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