335 KB31 KB2026Cambie, StijnTiwari, Ajayletnik:26številka:4, article p4.09str. 1-12DOI:10.26493/1855-3974.3643.9f6ISSN:1855-3974COBISSID_HOST:294231811URN:URN:NBN:SI:doc-UACOT9X9enUniverza na PrimorskemArs mathematica contemporaneabrisanje vozliščaŠoltés propertyŠoltésova lastnostuniform hypergraphuniformni hipergrafuteženi grafvertex deletionweighted graphWiener indexWienerjevo številoUniform Šoltés’ hypergraphs and Šoltés’ weighted graphs|A Šoltés’ hypergraph is a hypergraph for which the removal of any of its vertices does not change its total distance. We prove that every uniform Šoltés’ hypergraph has order at least 10, there exist uniform Šoltés’ hypergraphs for every order at least 10 and for almost every uniformity, and there exists a non-regular uniform Šoltés’ hypergraph. By also providing infinitely many weighted Šoltés’ graphs, we conclude that the Šoltés’ problem can be answered positively for most natural generalisations of graphsTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije