20.500.12556/RUP-22450 Nut digraphs 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. 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 orešni graf sredični graf ničelnost usmerjeni graf orešni digraf desno-orešni levo-orešni bi-orešni ambi-orešni inter-orešni desno-sredično vozlišče levo-sredično vozlišče spektri grafov true false false Angleški jezik Slovenski jezik Neznano 2026-01-09 15:49:21 2026-01-09 15:49:22 2026-01-13 03:05:39 0000-00-00 00:00:00 2026 0 0 str. 203-226 Vol. 383 15 Apr. 2026 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2026-04-15 519.17 0166-218X 10.1016/j.dam.2025.12.037 264177411 RAZ_Basic_Nino_2026.pdf RAZ_Basic_Nino_2026.pdf 1 D28F9C22CE19D03C7054F6E2F7513F0F 94ed3fda5bb7e6c6a7ee35248eaf5e61c246c624162c77477f00e8168be447e3 7766c3c1-ed6a-11f0-8639-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32641 https://www.sciencedirect.com/science/article/pii/S0166218X25007498?via%3Dihub 1 636f6ff6-ed6a-11f0-8639-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32640 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0