Nut digraphs

Bašić, Nino (avtor), Fowler, Patrick W. (avtor), McCarthy, Maxine M. (avtor), Potočnik, Primož (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: nut graph, core graph, nullity, directed graph, nut digraph, dextro-nut digraph, laevo-nut digraph, bi-nut digraph, ambi-nut digraph, inter-nut digraph, dextro-core vertex, laevo-core vertex, graph spectra
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: Str. 203-226
• Številčenje: Vol. 383
• PID: 20.500.12556/RUL-180418
• UDK: 519.17
• ISSN pri članku: 0166-218X
• DOI: 10.1016/j.dam.2025.12.037
• COBISS.SI-ID: 264177411
• Datum objave v RUL: 09.03.2026

Gradivo je del revije

• Naslov: Discrete applied mathematics
• Skrajšan naslov: Discrete appl. math.
• Založnik: Elsevier
• ISSN: 0166-218X
• COBISS.SI-ID: 25342464

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: orešni graf, sredični graf, ničelnost, usmerjeni graf, orešni digraf, desnoorešni digraf, levoorešni digraf, biorešni digraf, ambiorešni digraf, interorešni digraf, desnosredično vozlišče, levosredično vozlišče, spektri grafov